FOREST  MENSURATION 


C.  A.  SCHENCK,  Ph.D. 

Director  Biltmore  Forest  School,  and  Fort 
the  Biltmore  Estate 


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FOREST  MENSURATION 


By 

C.  A.  SCHENCK,  Ph.D. 

Director  Biltmore  Forest  School,  and  Forester  to 
the  Biltmore  Estate 


MCMV 


THE  UNIVERSITY  PRESS 
of  SEWANEE  TENNESSEE 


Digitized  by  the  Internet  Archive 

in  2009  with  funding  from 

NCSU  Libraries 


http://www.archive.org/details/forestmensuratioOOsche 


PREFACE 


Dear   Readers  : 

In  the  following  pages  an  attempt  is  made  to  treat  "Forest  Men- 
suration" from  a  scientific-mathematical  standpoint  as  well  as  from 
the  view  point  of  practical  application. 

Naturally,  pamphlets  of  as  restricted  a  character  as  this  treatise  on 
forest  mensuration  address  themselves  to  a  very  restricted  circle  of 
readers ;  and  the  expense  of  printing  is  never  covered  by  the  returns  from 
sales. 

Thus  it  becomes  necessary,  in  order  to  reduce  the  expense  of  pub- 
lication, to  omit  all,  or  practically  all,  lengthy  explanation  of  a  mathe- 
matical nature  which  the  teacher  at  a  forest  school  can  easily  supply 
in  the  course  of  his  lectures. 

The  present  Biltmore  pamphlet  on  Forest  Mensuration  is  intended, 
above  all,  to  assist  the  students  enlisted  at  the  Biltmore  School.  It  con- 
tains the  teacher's  dictation  which  the  students,  in  former  years,  were 
compelled  to  take  down  in  long  or  shorthand,  to  the  annoyance  of  both 
teacher  and  students. 

It  cannot  be  expected  that  a  present-day  lumberman  will  take  a  direct 
and  personal  interest  in  any  of  the  following  paragraphs.  Still,  in  con- 
servative forestry,  in  destructive  forestry,  and  in  any  other  business  en- 
terprise, the  truism  is  worth  remembering  that  "knowledge  is  the  best 
of  assets." 

Knowledge  certainly  forms  the  only  unalienable  factor  of  production. 

With  the  advent  of  high  stumpage  prices,  the  owner  of  woodland  will 
be  inclined  to  consider,  under  many  circumstances,  the  advisability  of 
forest-husbandry — an  idea  which  was  as  preposterous  in  past  decades  of 
superabundance  of  timber  as  the  raising  of  beef  cattle,  some  sixty  years 
ago,  in  the  prairies  then  abounding  in  buffalo. 

Financially  considered,  a  proper  outcome  of  forest-husbandry  is  and 
must  be  based  on  a  proper  application  of  the  theories  and  principles 
involved  in  forest  mensuration. 

I  shall  be  deeply  grateful  to  a  kind  reader  who,  discovering  mistakes 
or  incongruities  in  the  following  paragraphs,  will  take  the  trouble  of 
sending  me  a  timely  hint.  Most  truly, 

C.  A.  SCHENCK, 

Director  Biltmore  Forest  School,  and 
Forester  to  the  Biltmore  Estate. 
August  i,   1905. 


LECTURES  ON  FOREST  MENSURATION 


SYNOPSIS  OF  CONTENTS  BY  PARAGRAPHS. 


Par. 


I.     Definition  and  subdivision. 


Par. 

II. 

Par. 

III. 

Par. 

IV. 

Par. 

V. 

Par. 

VI. 

Par. 

VII. 

Par. 

VIII. 

Par 

IX. 

Par. 

X. 

Par. 

XI. 

Par. 

XII. 

Par. 

XIII. 

Par. 

XIV. 

Par. 

XV. 

Par. 

XVI. 

Par. 

XVII. 

Par. 

XVIII. 

Par. 

XIX 

Par. 

XX. 

Par. 

XXI. 

Par. 

XXII. 

Par. 

XXIII. 

Par. 

XXIV. 

Par. 

XXV. 

Par. 

Si 
XXVI. 

Par. 

XXVII. 

Par. 

XXVIII. 

Par. 

XXIX. 

Par. 

XXX. 

Par. 

XXXI. 

Par. 

XXXII. 

Par. 

XXXIII. 

Par. 

XXXIV. 

CHAPTER  I.— VOLUME. 

Section  I.— Volume  of  Trees  Cut  Down. 

Units  of  volume. 

Mathematical  form  of  trees. 

Cylinder 

Apollonian  Paraboloid. 

Cone. 

Ne ill's  paraboloid. 

Riecke's,  Huber's  and  Smalian's  formule. 

Hossfeld's  formule. 

Simony's  formule. 

Sectional  measurement. 

Measuring  the  length  of  a  log. 

Measuring  the  sectional  area. 

Instruments  for  measuring  diameters. 

Units  of  log  measurement  in  the  United  States. 

Board-rules. 

Standard-rules. 

Cubic  foot-rules. 

Equivalents. 

Xylometric  method. 

Hydrostatic  method. 

Factors  influencing  the  solid  contents  of  cordwood. 

Reducing  factors  for  cordwood. 

Local  peculiarities  with  reference  to  stacked  wood. 

Bark. 

Section  II. — Volume  oe  Standing  Trees. 

Methods  of  obtaining  the  volume  of  standing  trees. 

Helps  and  hints  to  find  the  volume  of  standing  trees. 

Scientific  methods  of  ascertaining  the  cubic  contents  of 
standing  trees  by  mere  measurement. 

Form  factor  method. 

Kinds  of  form  factors  mathematically. 

Kinds  of  common  form  factors  in  European  practice. 

Means  for  exact  mensuration  of  standing  trees. 

Measuring  the  height  of  a  standing  tree. 

Factors  influencing  the  exactness  of  hypsometrical  ob- 
servations. 


VI. 


Forest  Mensuration 


Par. 

XXXV. 

Par. 

XXXVI. 

Par. 

XXXVII. 

Par. 

XXXVIII 

Indirect  mensuration  of  diameter. 
Pressler's  telescope. 
Auxiliaries  for  calculation. 
Tree  volume  tables. 


Par. 


XXXIX. 


Par. 

XL. 

Par. 

XLI. 

Par. 

XLII. 

Par. 

XLIII. 

Par. 

XLIV. 

Par. 

XXV. 

Par 

XL  VI. 

Par. 

XLVII. 

Par. 

XLVIII. 

Par. 

XLIX, 

Par. 

L. 

Par 

LI. 

Par. 

LII. 

Par. 

LIU. 

Par. 

LIV. 

Par. 

LV. 

Par. 

LVI. 

Par. 

LVII. 

Par. 

LVIII. 

Par. 

LIX. 

Par. 

LX. 

Par. 

LXI. 

Par. 

LXII. 

Par. 

LXIII. 

Par. 

LXIV. 

Par. 

LXV. 

Par. 

LXVI. 

Par. 

LXVII. 

Par. 

LXVIII. 

Section  III. — Volume  of  Forests. 

Synopsis    of  methods   for   ascertaining   the   volume    of 

forests. 
Estimation  of  forest  volume. 
Principles  underlying  the  exact    mensuration  of  forest 

volume. 
Field  work  for  exact  valuation  surveys. 
Basal  assumptions. 
Selection  of  sample  trees. 
Draudt-Urich  method. 
Robert  Hartig  method. 
Average  sample-tree  method. 

Exact  mensuration  without  cutting  sample  trees. 
Combined  measuring  and  estimating. 
Form  factor  method. 
Form  height  method. 
Volume  table  method. 
Yield  table  method. 
Distance  figure. 

Algon's  Universal  Volume  Tables. 
Schenck's  graphic  method. 
Factors  governing  the  selection  of  a  method  of  valuation 

survey 
Factors  influencing  the  selection  of  sample  plots. 
Sir  D.  Brandis  method. 
Pinchot-Graves  method  on  Webb  estate. 
The  gridironing  method. 
Forest  reserve  methods. 
Sample  squares. 
Pisgah  Forest  method  of  1896. 
Pisgah  Forest  method  for  stumpage  sale,  bark  sale  and 

lumbering  operations. 
Henry  Gannett's  method,  adopted  for  the  XHth  census. 
A  forty  method  used  in  Michigan. 
Dr.  Fernow's  forty  method  used  at  Axton. 


CHAPTER  II— AGE  OF  TREES  AND  OF  FORESTS. 

Par.  LXIX.     Age  of  trees  cut  down. 

Par.  LXX.     Age  of  standing  trees. 

Par.  LXXI.     Age  of  a  forest. 


Forest  Mensuration 


vn. 


Par. 


CHAPTER  III.— INCREMENT  OF  TREES  AND  OF  FORESTS. 

Section  I. —  Increment  of  a  Tree. 

The  kinds  of  increment. 

Height  increment. 

The  current  height  increment. 

The  average  height  increment. 

Relative  increment  of  the  height. 

Diameter  increment. 

Sectional  area  increment. 

Relative  increment  of  diameter  and  of  sectional  area. 

Volume  increment. 

Section  analysis. 

Noerdlinger's  paper-weight  method. 

Schenck's  graphic  tree  analysis. 

Wagener's  method  and  stump  analysis. 

Pressler's  method. 

Breyman's  method. 

Factors  influencing  the  cubic  volume  increment. 

Volume  increment  percentage  of  standing  trees. 

Interdependence  between  cubic  increment  and  increment 

in  feet  b.  m.,  Doyle. 
Construction  of  volume  tables. 


Par. 

LXXII. 

Par. 

LXXIII. 

Par. 

LXXIV. 

Par. 

LXXV. 

Par. 

LXXVI. 

Par. 

LXXVII. 

Par. 

LXXVIII. 

Par. 

LXXIX. 

Par. 

LXXX. 

Par. 

LXXXI. 

Par. 

LXXXII 

Par 

LXXXIII. 

Par. 

LXXXIV. 

Par. 

LXXXV. 

Par. 

LXXXVI. 

Par. 

LXXXVII. 

Par. 

LXXXVIII. 

Par. 

LXXXIX. 

xc. 


Par. 

XCI. 

Par. 

XCII. 

Par. 

XCIII. 

Par. 

XCIV. 

Par. 

xcv. 

Par. 

XCVI. 

Par. 

XCVII. 

Par. 

XCVIII. 

Par. 

XCIX. 

Section  II. —  Increment  of  a  Wood. 

Increment  of  forests. 

Method  of  construction  of  normal  yield  tables. 

Gathering  data  for  normal  yield  tables. 

Normal  yield  tables,  their  purpose  and  contents  abroad. 

Retrospective  yield  tables. 

Yield  tables  of  the  Bureau  of  Forestry. 

The  increment  of  a  woodlot. 

Ascertaining  the  increment  of  woodlots  by  sample  trees. 

Current  increment  ascertained  from  average  increment. 


Par. 
Par. 


CHAPTER  IV.— LUMBER. 
C.     Units  of  lumber  measure. 
CI.     Inspection  rules  and  nomenclature. 


Par. 


CHAPTER  V.— STUMPAGE-VALUES. 
CII.     Stumnaaie-values. 


FOREST   MENSURATION 


PARAGRAPH     I. 

DEFINITION    AND    SUBDIVISION. 

Definition :  By  "Forest  Mensuration,"  the  forester  ascertains  the  vol- 
ume, the  age,  the  increment  and  the  stumpage  value  of  trees,  parts  of 
trees  and  aggregates  of  trees.  As  a  branch  of  forestry,  forest  mensura- 
tion may  be  divided  into  the  following  five  parts : 

I.     Determination   of  volume   of   trees   cut   down,   of   standing   trees 
and  of  forests. 
II.     Determination  of  age  of  trees  and  of  forests. 

III.  Determination  of  increment  of  trees  and  of  forests. 

IV.  Determination  of  sawn  lumber. 
V.     Determination  of  stumpage  value. 

Circular  445  of  the  Bureau  of  Forestry  defines  mensuration  as  "the 
determination  of  the  present  and  future  product  of  the  forest." 

American  literature  is  found  in  Bulletin  20,  Division  of  Forestry;  Bul- 
letin 36,  Bureau  of  Forestry ;  S.  B.  Green,  page  132 ;  Lumber  &  Log  Book 
and  Lumberman's  Handbook,  edited  by  the  "American  Lumberman." 


CHAPTER  I.— VOLUME. 

SECTION  I.— VOLUME  OF  TREES  CUT  DOWN. 
PARAGRAPH  II. 

UNITS     OF     VOLUME. 

The  volume  of  a  tree  or  of  a  tree  section  is  expressed : 

1.  For   scientific   purposes,   on   the  basis   of  exact   measurements,   in 

cubic  feet  or  cubic  meters. 

2.  For  practical  purposes,  by  estimates  according  to  local  usage,  often 

assisted    by    partial    measurement,    in    local    units    (feet    board 
measure;  standards;  cords;  cubic  feet;  cord  feet;  etc.). 

PARAGRAPH    III. 

MATHEMATICAL     FORM     OF     TREES. 

Trees  do  not  grow,  like  crystals,  according  to  purely  mathematical  laws. 
Tree   growth   is   deeply  influenced   by   individuality,   by  surroundings,   by 
accidental  occurrences,  etc. 
2 


2  Forest  Menstiration 

The  body  of  a  tree,  considered  as  a  conoid  (a  solid  body  formed  by 
the  revolution  of  a  curve  about  an  axis),  is  very  complicated,  being 
formed  by  a  curve  of  high  power.  This  is  the  case  even  in  straight  and 
clear  boled  conifers.  The  tree  bole  shows,  however,  in  certain  sections 
of  its  body  frequently  a  close  resemblance  to  a  truncated  neilloid,  cylinder, 
paraboloid  and  cone. 

The  longitudinal  section  of  conoids  is  outlined  by  a  curve  correspond- 
ing with  the  general  equation 

y2  =  px« 
in  which  y  is  the  ordinate    (corresponding  with  the  radius  of  the  basal 
area),    x   the   abscissa    (representing   the    height    of    the    conoid),    n    the 
power  of  the  curve ;   whilst  p  is  merely  a  constant  factor.     The  volume 
v  of  the  conoid  is  obtained  by  integral  calculus : 

v  _  y2  7tx 
n  +  1 

It  is  equal  to  sectional  area,  s,  times  height,  h,  over  (n-j-i). 

The  truncated  volumes  are  developed  by  deducting  a  small  top  conoid 
from   a    large    total    conoid. 

Stht  — s2h2 

vol.  tronc.= 

n  +  1 

In  the  general  curve  equation 

y2  =  px« 

we  find  represented : 

A.  For  n  equal   to  o,   the  cylinder; 

B.  For   n   equal    to    i,    the   Apollonian   paraboloid,    wherein   the    ratio 

between  sectional  area  and  height  is  constant ; 

C.  For  n  equal   to  2,   the  cone,   wherein   the  ratio  between   radius  of 

sectional  area  and  height  is  constant; 

D.  For  n  equal  to  3,  Neill's  paraboloid,  the  truncated  form  of  which 

is  found  at  the  basis  of  our  trees. 

The  top  of  the  tree  resembles  a  cone  or  Neilloid ;  the  main  bole 
resembles  the  cylinder  or  the  Apollonian  paraboloid. 

The  cross  section  (see  Par.  XIII.)  through  a  tree  taken  perpen- 
dicular to  its  axis  shows  a  more  or  less  circular  form.  Near 
sets  of  branches  and  near  the  roots,  however,  the  outline  is 
irregular.  The  center  of  the  circle  usually  fails  to  coincide  with 
the  axis  of  the  tree. 

PARAGRAPH   IV. 

CYLINDER. 

The  cubic  contents  v  of  a  cylinder  are  equal  to  the  height  h  of  the 
cylinder,  multiplied  by  the  sectional  area  J  of  the  cylinder. 

vol.  cylinder  =  h.s 


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Forest  Mensuration 


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PARAGRAPH    V. 

APOLLONIAN     PARABOLOID. 

The  volume  v  of  the  Apollonian  paraboloid  is  equal  to  height  multi  ■ 
plied  by  Yi  sectional  area,  or  equal  to  ^  of  a  cylinder  having  the  same 
height  and  the  same  basal  area. 

h.s 
vol.  apol.  =  - — 

The  volume  t  of  the  truncated  Apollonian  paraboloid  may  be  ascer- 
tained as : 

A.  Height   of  trunk   times  arithmetical   mean   of   top   sectional   area 

and  base  sectional  area. 

st  +  s„ 

t.  apol.  =  h 

2 

B.  Height  of  trunk  times  sectional  area  in  the  midst  of  the  trunk. 

t.  apol.  =  h.sj 


PARAGRAPH   VI. 

CONE. 

The  volume  of  the  ordinary  cone  is  equal  to  height  of  cone  times  1/3 
sectional  area  at  the  base. 

h.s 
vol.  coDe  =  — 
3 

The  volume   t  of  the  truncated  cone  is  equal   to    1/3  height  of  trunk 
times  sum  total  of  top  sectional  area  si,  basal  sectional  area  S2,  and  V  si  S2 

h  t/ 

t.  cone  =  —  (Sj  +  s2  +  V  s1s2) 


PARAGRAPH  VII. 

NEILL's     PARABOLOID. 

The  volume  of  the  Neilloid  equals  Y\  of  its  height  times  sectional  area 
at  the  base. 


vol.  neil.  = 


h.s 


The  volume  of  the  truncated  neilloid  t  equals 

t.  neil.  =  — (  st  +  s2  +  &&^*   [^ s"7+  f  s^]  J 

wherein  h  denotes   the  height  of  the  trunk;   Sj  and  s2  the  top  sectional 
area  and  the  basal  sectional  area  of  the  trunk. 


\{H  js\V 


Forest  *minsuration 


X 


PARAGRAPH  VIII. 
riecke's,  huber's  and  smalian's  formule. 

J 

*     Formules  of  practical  and  scientific  application,  used  here  and  abroad, 
to  ascertain  the  contents  of  logs,  are  those  published  by  Smalian,  Riecke 
and  Huber. 
^M»^V        Riecke's  formula  holds  good  for  n  equal  to  o,  I  and  2,  and  is  almost 
correct  for  the  neilloid. 

Smalian  over-estimates  and  Huber  under-estimates  the  actual  contents 
of  the  truncated  cone  and  of  the  truncated  neilloid. 

h 
Riecke — Vol.   of  trunk  =  —  (Sj  +  4si  +  s2) 

6 

Huber — Vol.    of    trunk  =  h.sj 

h 
Smalian — Vol.  of  trunk  =  —  (st  -f-  s2) 

Si  designates  the  sectional  area  in  the  midst  of  the  trunk,  whilst  si  and  S2 
represent  basal  sectional  area  and  top  sectional  area. 

PARAGRAPH  IX. 

hossfeld's  formule. 
The  formule  given  by  Hossfeld  is : 

h 
Vol.  of  trunk   =  —  (3  S|  +  s2) 
4 

It  holds  good  for  cylinder,  cone  and  paraboloid.  Si  designates*  the  sec- 
tional area  at  J  of  the  height  of  the  trunk. 

PARAGRAPH   X. 

simony's   formule. 

Simony's  formule  requires  measurements  of  sectional  areas  at  J4,  *A 
and  24  of  the  height  of  the  trunk,  thus  avoiding  the  irregularities  caused 
by  the  roots  at  the  base  and  by  the  branches  at  the  top  of  a  tree-trunk. 

h 
Vol.  of  trunk   =  —  (2  S|  —  sj  -f  2  S|  ) 

This  formule  holds  good  for  the  four  standard  conoids. 


PARAGRAPH  XL 

SECTIONAL  measurement. 

The  formules  given  in  Paragraphs  III.  to  X.  have,  in  C.  A.  Schenck's 
opinion,  a  historic  interest  only  when  applied  to  whole  trees.  It  is  much 
safer  to  ascertain  the  volume  of  a  tree  bole  by  dissecting  it  into   (imag- 


Forest  Mensuration  5 

inary)  log  sections  of  equal  length,  considering  each  of  such  sections 
as  a  cylinder  or  as  a  truncated  paraboloid.  The  shorter  the  length  of 
the  sections,  the  greater  the  accuracy  of  the  result.  In  scientific  research, 
the  length  of  a  section  varies  from  5  feet  to  10  feet.  Obviously,  at  the 
top  of  the  bole  an  uneven  length  is  left,  which  it  might  be  wise  to  ascer- 
tain as  a  cone  (or  paraboloid — Bulletin  20).  The  volume  of  the  total 
bole,  from  stump  to  tip,  equals,  if  the  length  of  such  full  section  is  "\," 
and  that  of  the  top  cone  is  "b,"  and 

1 )  if  sectional  areas  si,  S2,  S3, sn  are  measured  at  the  big  end  of  each 

section : 

vol     bole  =-(s1+2s2  +  2s, +  sn  )  +  -~ 

2)  if  sectional  areas  Si,Sn,  Sm, sm  are  measured  in  the  midst  of  each 

full  section,  and  sectional  area  sn  at  the  basis  of  the  top  cone : 

b.Sn 
vol.   bole  =  1  (si  -f-  Sn  -f-  Sin +  sm)  -f 

The  former  formula  is  based  on  Smalian  and  the  latter  on  Huber. 

In  a  similar  way,  and  with  still  greater  accuracy,  the  more  complicated 
formulas  of  Riecke,  Hossfeld  and  Simony  might  be  adapted  to  sectional 
measurements. 

Remark  :  If  the  diameter  in  the  middle  of  a  log  is  larger  than  the 
arithmetical  mean  of  the  end  diameters,  then  the  log  contains  more  vol- 
ume than  the  truncated  cone,  and  vice  versa. 

If  the  sectional  area  at  the  midst  of  the  log  is  larger  than  the  arith- 
metical mean  of  the  end  sectional  areas,  then  the  log  contains  more 
volume  than  the  truncated  paraboloid,  and  vice  versa.  * 

PARAGRAPH    XII. 

MEASURING    THE    LENGTH    OF    A    LOG. 

The  length  of  a  log  is  measured  with  tape,  stick  or  axe  handle.  In 
American  logging,  logs  are  usually  cut  in  lengths  of  even  feet,  increased 
by  an  addition  of  two  inches  to  six  inches,  which  addition  allows  for 
shrinkage,  for  season  checks,  for  damage  to  the  log  ends  inflicted  by 
snaking  or  driving,  and  for  the  trimming  in  the  saw  mill  required  to 
removed  such  end  defects. 

In  Continental  Europe,  the  standard  log  lengths  are  multiples  of  even 
decimeters.     An  excess-length  of  up  to  eight  inches  is  neglected. 

Crooked  logs  are  made  straight  by  deductions  either  from  the  length 
or  from  the  diameter.  Crooked  trees  should  be  dissected  into  very  shor*- 
logs. 

The  standard  length  of  a  New  England  log  is  13  feet. 

In  the  case  of  big  logs,  great  care  must  be  taken  by  the  sawyers  to 
obtain  end-cuts  perpendicular  to  the  axis  of  the  log. 

The  sum  of  the  lengths  of  logs  cut  from  a  tree  is  termed  "used  length." 
The  total  length  of  that  portion  of  a  bole  which  is  merchantable  under 
given  conditions  is  called  "merchantable  length." 


^N**JsJL 


^%>  V  %    f  «OA^*^ 


6  Forest  Mensuration 

PARAGRAPH  XIII. 

MEASURING    THE    SECTIONAL    AREA. 

The  sectional  areas  are  ascertained  with  the  help  of  measuring  tape, 
caliper,  tree  shears,  tree  compasses,  Biltmore  measuring  stick,  etc. 

The  sectional  area  is  thus  derived  from  the  measurement  either  of  the 
diameter  or  of  the  circumference. 

For  exact  scientific  investigations  the  planimeter  or  the  weight  of  an 
even-sized  piece  of  paper  may  be  used. 

It  is  best  to  consider  the  sectional  area  of  a  tree  as  an  ellipse,  the 
surface    of    which    is : 

TV 

surface  =  —  D.d, 
4 

the  big  diameter  D  being  measured  vertically  to  the  small  diameter  d. 

Usually,   however,   the   average   diameter  of  the   tree  at  a  given  point 

is  found  as  the  arithmetical  mean  of  the  big  and  small  diameter  at  that 

point  measured  crosswise  and  not  as  the  square  root  of  the  product  of 

such  diameters.     Since 

D  +  d        , 

the  average  diameter  is  invariably,  though  slightly,  over-estimated  by 
crosswise  measurement.  Hence  it  is  wise  to  drop,  as  an  arbitrary  offset, 
the  excess  of  fractions  of  inches  over  full  inches. 

The  arithmetical  mean  of  the  sectional  areas  belonging  to  diameters 
measured  crosswise  leads  to  still  greater  mistakes. 

» 

PARAGRAPH  XIV. 

INSTRUMENTS    FOR    MEASURING   DIAMETERS. 

Log  calipers  are  made  of  pyrus  wood  or  of  metal.  American  make 
(Morley  Bros.,  Saginaw,  Mich.)  cost  $4.00  each.  The  moving  leg  of  the 
caliper  is  kept  in  place  by  a  spring  or  a  screw  or  a  wedge. 

The  best  European  makes  are  the  "Friedrich"  and  the  "Heyer  and 
Staudinger."  Wimmenauer's  "addition-caliper".  counts  the  trees  and  adds 
their  sectional  areas  automatically. 

Short  legged  calipers,  named  "Dachshunds"  by  C.  A.  Schenck,  can  be 
used  for  trees  the  radius  of  which  exceeds  the  length  of  the  legs.  The 
diameter  is,  in  that  case,  indirectly  found  by  the  help  of  the  secant  joining 
the  tips  of  the  legs,  which  are  about  5"  long. 

"Tree  compasses,"  opening  from  six  inches  to  thirty-six  inches,  and 
made  of  nickel-plated  steel,  cost  (at  Morley  Bros.)  $7.50.  "Tree  shears" 
(Treffurth)  find  the  angle  formed  by  the  shear-legs  when  pressed  against 
the  tree  and  directly  derive  therefrom  the  diameter  or  the  sectional  area 
of  the  tree. 

The  "diameter  tape"  slung  around  the  tree  usually  yields  too  large  a 
diameter,  since  the  circle  embraces  the  maximum  of  surface  by  the  min- 
imum of  length. 


Forest  Mensuration 


The  "Biltmore  Measuring  Stick"  can  be  well  used  in  timber  cruising. 
It  requires  the  exact  adjustment  of  distance  between  eye  and  fist  of  ob- 
server (usually  26  inches),  and  gives  directly  the  diameter  at  the  point 
of  the  stick  where  the  sight  line  passes  the  tree  tangentially.  The  stick 
is  held  horizontally  against  the  tree. 

26-inch  Biltmore  Measuring  Stick. 


Length  on 
the  stick. 

Diameter 
with  bark. 

Contents  of 
butt  log. 

Contents  of 
two  logs. 

Contents  of 
three  logs. 

2.8" 
5-4" 
7-7" 
9.9" 

3" 
6" 

9" 
12" 

Allowing   three   inches    for   bark   and 
three  inches  for  taper,  per  log;     assuming 
thst  all  logs  are  14'  long. 

1 1.9" 
13-8" 
15.6" 
17.3" 

15" 
18" 
21" 
24" 

22  ft.  b.  m. 

56  "       " 
106  "       " 
171   "       " 

29  ft.  b.  m. 

78  "       " 
162  "       " 

277  "       " 

39  ft.  b.  m. 
85  "      " 
184  "      " 

333  "       " 

18.9" 
20.4" 
21.9" 
23.3" 

27" 
30" 

33" 
36" 

253  "       " 
350  *'       " 
463  "       " 

591   "      " 

424  " 
603  "       " 
813  "       " 
1054  "       " 

530  " 

774  " 
1066  "       " 
1404  "       " 

Mr.  Snead  recommends  to  measure  the  circumference  outside  the  bark 
at  the  big  end  and  to  divide  the  result  by  4.  He  claims  that  the  quotient 
yields  the  diameter  at  the  small  end  inside  bark  in  such  a  way  as  to  offset 
mistakes  made  by  Doyle,  who  under-estimates  small  logs  and  over-esti- 
mates big  logs.  Snead's  suggestion  is  good,  provided,  that  the  cross  sec- 
tion of  the  log  is  fairly  circular,  and  that  the  difference  between  the  small 
diameter  inside  bark  at  the  small  end  and  the  big  diameter  outside  bark 
at  the  big  end,  amounts  to  about  7  inches. 


Diameter  at  small  end 
inside  bark. 


10  inches. 

15 
20 

25 

30 

35 


Contents  of  16  foot  logs,  in  feet  b.m. 


Doyle. 

Snead. 

Actual  saw  cut. 

36' 

8i' 

70' 

121' 

169' 

157' 

256' 

289' 

279' 

441' 

441' 

436' 

676' 

625' 

628' 

961' 

841' 

856' 

The  multiples  of  sectional  area  (derived  from  the  diameter  in  inches, 
but  expressed  in  square  feet)  by  length  of  log  are  readily  obtained  from 
cylinder  tables  published  by  various  authors.  The  log  scale  or  log  rule 
used  by  the  lumbermen  (Lufkin  rule)  gives  at  a  glance  the  contents  of 
logs  8  to  20  feet  long,  according  to  their  diameter. 


8  Forest  Mensuration 

PARAGRAPH  XV. 

UNITS    OF    LOG     MEASUREMENT    IN     THE    UNITED    STATES. 

The  units  of  log  measurement  used  in  the  United  States  differ  greatly. 
Graves'  Handbook  gives  43  "rules."  The  rules  can  be  subdivided  into 
three  main  grops : 

Board  feet  group    (Par.   XVI.)  ; 
Standard  log  group    (Par.  XVII.)  ; 
Artificial  cubic  foot  group   (Par.  XVIII. ). 

PARAGRAPH  XVI. 

BOARD-RULES. 

A  foot  board  measure  is  a  superficial  foot  one  inch  thick,  in  boards  one 
inch  or  more  in  thickness.  It  is  a  superficial  foot,  irrespective  of  thick- 
ness, in  boards  less  than  one  inch  in  thickness. 

The  "board  rules"  merely  guess  at  the  number  of  feet  board  measure 
obtainable  from  logs  of  a  given  diameter.  The  guess  is  based  upon 
either  graphical  considerations,  circles  of  specified  diameters  being  sub- 
divided into  parallelograms  1%  inch  thick  (diagram  method),  or  else 
on  mathematical  considerations,  with  a  view  to  the  fact  that  a  cubic  foot 
of  timber  should  theoretically  yield  12  board  feet  of  lumber,  whilst  the 
actual  loss  for  slab,  saw  kerf,  etc.,  will  reduce  the  output  by  30%  to 
50%.  In  the  Biltmore  band  saw  mill,  by  over  one  thousand  tests,  the 
actual  loss  for  logs  12  inches  to  40  inches  in  diameter  has  been  found  to 
amount  to  30%,  or  close  to  1/3.  Consequently,  it  is  safe  to  say  that  the 
band  saw  obtains  from  a  cubic  foot  of  log  8  board  feet  of  lumber.  * 

The  number  of  board  feet  which  a  log  actually  yields  depends  on: 

1.  The  actual  cubic  volume  of  a  cylinder  having  the  length  and  small- 
est diameter  inside  bark  of  the  log. 

2.  The  defects  of  the  log  (heart  rot,  wind  shake,  bad  knots,  crooks), 
which  are  usually  eliminated  by  edger  or  trimmer. 

3.  The  gauge  of  the  saw,  on  which  the  saw  kerf  depends.  The  kerf 
of  band  saws  amounts  to  Y%  inch,  of  circular  saws  to  usually  *4  inch,  of 
inserted  tooth  saws  (of  large  diameter)  to  y%  inch,  of  resaws  to  1/16 
inch. 

4.  The  exactness  of  the  work,  especially  depending  on  trueness  of  saw, 
proper  lining  of  saw  and  sawyer's  skill ;  further,  on  the  exactness  of  the 
setworks. 

5.  The  thickness  of  boards  obtained ;  the  minimum  width  of  boards 
permitted ;  the  amount  of  lumber  wasted  in  the  slabs ;  shrinkage  in  drying. 

The  following  table  compares  the  contents  of  logs  in  cubic  feet  with 
their  contents  in  feet  board  measure  as  found  by  C.  A.  Schenck  through 
a  thousand  tests  of  actual  yield  in  yellow  poplar,  as  given  by  Doyle's 
rule  and  by  Lumberman's   Favorite  rule. 

The  figures  given  in  columns  c,  f  and  i  show  the  contents  of  a 
log  in  feet  board  measure  after  Schenck's  findings,  Doyle's  and  Favorite 


Forest  Mensuration 


9 


rules.  They  are  converted  into  cubic  feet  (columns  d,  g,  and  j)  by  divid- 
ing by  12.  The  loss  incurred  in  sawing  is  shown  by  percentages  (col- 
umns e,  h,  k)  representing  the  ratio  between  the  actual  cubic  con- 
tents of  a  log  (as  given  in  column  b),  and  the  cubic  contents  of  inch 
boards  (columns  d,  g,  j)  obtained  from  such  log. 

It  will  be  observed  that  the  loss  in  the  actual  yield  according  to  Schenck 
forms  a  nearly  constant  proportion  of  the  cubic  contents  of  a  log  in  the 
case  of  all  diameters,  whilst,  according  to  Doyle's  and  Favorite  rules,  the 
figures  of  loss  vary  greatly. 

The  table  refers  to  logs  12'  long  sawed  into  i-inch  boards. 


Diameter 

Contents. 
Cubic 

Schenck. 

Doyle. 

Favorite. 

of 

Log. 

Feet. 

Feet 

Cubic 

Loss 

Feet 

Cubic 

Loss 

Feet 

Cubic 

Loss 

Inches. 

b.  m. 

Feet. 

0/ 

/o 

b.  m. 

Feet. 

% 

b.  m. 

Feet. 

% 

a. 

b. 

c. 

d. 

e. 

f. 

g- 

h. 

i. 

j- 

k. 

8 

4-2 

53 

6-5 
8.0 

12 

0.9 
1.6 

76 

9 
10 

19 

27 

70 

2.3 
4.0 

65 
61 

1 1 

37 
48 

12 

9-4 

78 

6-5 

31 

57 

49 

4-i 

56 

13 

11 .0 

96 

S.o 

27 

61 

5-i 

54 

62 

5-2 

53 

14 

12.8 

112 

9-3 

27 

75 

6-3 

5i 

74 

6.2 

52 

15 

14-7 

129 

10.7 

27 

9i 

7.6 

48 

90 

7-5 

49 

16 

16.8 

146 

12.  2 

27 

108 

9.0 

46 

107 

8.9 

46 

17 

18.9 

162 

13-5 

29 

127 

10.6 

44 

125 

10.4 

45 

iS 

21 .2 

1  So 

15.0 

29 

147 

12.3 

42 

148 

12.3 

42 

19 

23.6 

197 

16.4 

30 

169 

14. 1 

40 

170 

14.2 

39 

20 

26.2 

212 

17-7 

32 

192 

16.0 

39 

186 

15-5 

41 

21 

28.9 

230 

19.2 

34 

217 

18. 1 

37 

214 

17.8 

38 

22 

3i -7 

248 

20.7 

35 

243 

20.3 

36 

243 

20.3 

36 

23 

34-6 

266 

22.  2 

36 

271 

22.6 

35 

268 

22.3 

36 

24 

37-7 

298 

24.8 

34 

300 

25.0 

33 

294 

24- 5 

35 

25 

40.9 

33i 

27.6 

32 

33i 

27.6 

32 

326 

27.2 

33 

26 

44-2 

362 

30.2 

32 

363 

303 

3i 

35S 

29.  S 

33 

27 

47-7 

394 

32-9 

3i 

397 

33- 1 

30 

390 

32.5 

32 

28 

51-3 

422 

35-2 

3i 

432 

36.0 

30 

422 

35-2 

3i 

29 

55-0 

456 

38.0 

3i 

469 

39- 1 

29 

44S 

37-3 

32 

30 

58.9 

488 

40.7 

31 

507 

42-3 

28 

474 

39-5 

33 

3i 

62.9 

5i8 

43-2 

3i 

547 

45-6 

27 

509 

42.4 

33 

32 

67.0 

556 

46.3 

3i 

588 

49.0 

27 

544 

45-3 

32 

33 

71-3 

596 

49-7 

30 

631 

52.6 

26 

5S9 

49.1 

3i 

34 

75-7 

634 

52.8 

30 

675 

56.3 

26 

634 

52.8 

30 

35 

80.2 

670 

55-8 

30 

721 

60. 1 

25 

662 

55-2 

3i 

36 

84.8 

710 

59-2 

30 

768 

64.0 

25 

690 

57-5 

32 

37 

89.6 

755 

62.9 

30 

817 

68.1 

24 

734 

61 .2 

32 

38 

94-5 

S06 

66.7 

29 

867 

72.3 

23 

778 

64.8 

3i 

39 

99-5 

850 

70.8 

29 

910 

75-8 

24 

824 

68.7 

3i 

40 

104.7 

901 

75-0 

28 

972 

81.0 

23 

870 

72.5 

3i 

From  column  e  it  is  evident  that  the  bandsaw  wastes  close  to  1/3 
of  the  cubic  contents  of  a  cylindrical  log,  or  4'  b.  m.  out  of  every  cubic 
foot. 

Consequently,   from  hardwood  logs   12  feet  to   16  feet  long,   the  band- 


io  Forest  Mensuration 

saw    will    obtain    the    following   actual   number    of    feet   b.    m.    (in   4/4" 
thickness)  : 

D2  X  0.78  X  12  X  8 
(a)  from  12  foot  logs:  ,  almost  equal  to  D2X-5 


144 

D2 

X  0.78  X  14  X  8 

144 

W 

X  0.78  X  16  X  8 

(c)    from  16  foot  logs:  ,  almost  equal  to  D2X-7 

144 

Hence  it  can  be  stated  generally,  for  logs  of  medium  length  "L,"  that 
their  contents   in  band-sawed   inch   lumber   approximate 

D2       L  — 2 

—  X  feet  b.  m. 

10  2 

PARAGRAPH  XVII. 

STANDARD    RULES. 

_  Yv.M  The  standard  rules  do  not  estimate  the  contents  of  a  log  according  to 

output  in  board  feet,  but  compare  the  log  with  a  local  average  log.  Such 
average  logs  used  to  have,  in  the  Northeast,  formerly,  a  diameter  of 
either  19  inches  (Adirondacks)  or  22  inches  (Saranac  River)  or  24 
inches,  and  were  in  all  cases  13  feet  long. 

The   19  inch  standard  log  rule  is  known  as  Dimick's   rule.     Here  the 

"standard"  or  "market"  is  a  log  13  feet  long  and  19  inches  thick.     On  a 

"b<\v,  o-i  i.*f       22  jnch  base  ft  js  T^  feet  long  and  22  inches  thick.     On  a  24  inch  base 

*"!  <^     it  is  13  feet  long  and  24  inches  thick. 

\  The  standard  contents  of  a  given  log  are  found  by  dividing  the  cubic 

'volume  of  the  standard  log  into  the  cubic  volume  of  the  given  log. 

d2X  h 

v  (in  standards)  equals: 

193  X  13 

Scientifically  and  mathematically  the  standard  rules  are  superior  to 
the  board  rules.  One  market,  at  a  19  inch  base,  is  generally  considered 
equivalent  to  200  board  feet ;  at  a  22  inch  base,  to  250  board  feet ;  at  a 
24  inch  base,  to  300  board  feet. 

It  is  easily  shown  that  the  output  of  small  logs  is  not  as  badly  under- 
estimated, and  the  output  of  big  logs  not  as  badly  over-estimated  on  the 
basis  of  standard  rules,  as  is  the  case  when  Doyle's  rule  alone  is  applied. 

PARAGRAPH    XVIII. 

CUBIC    FOOT-RULES. 

In  a  third  group  of  rules,  a  new  unit,  the  "artificial  cubic  foot,"  is 
introduced.  This  group  of  rules  is  established  by  law  in  Maine  and  New 
Hampshire.     (See  Graves'   Handbook,  page  45.) 


Forest  Mensuration  II 

The  artificial  cubic  foot  corresponds  with  a  log  12  inches  long  and 
16  inches  thick,  which  naturally  contains  1.4  cubic  feet.  The  rule  as- 
sumes that  40/140  or  28.5%  of  a  log  goes  to  waste  in  the  sawing  process 
as  dust  or  slab. 

To  quickly  transform  artificial  cubic  feet  into  board  feet,  the  laws  pre- 
scribe certain  arbitrary  equivalents,  instead  of  allowing  12  board  feet 
to  equal  one  artificial  cubic  foot  of  timber.  In  New  Hampshire,  10  board 
feet  equal  one  artificial  cubic  foot.  In  Maine,  11.5  board  feet  equal  one 
cubic  foot.  The  rules  might  be  used  in  connection  with  a  cylinder  table, 
deducting  28.5%  from  the  table  data  and  multiplying  the  remainder  by 
10   or  by    11. 5. 

Remark  :  According  to  the  Forest  Reserve  Manual,  logs  over  24  feet 
long  are  treated  as  16  foot  logs  and  fractions  thereof. 


PARAGRAPH  XIX. 

EQUIVALENTS. 

One  cubic  meter  equals  35.316  feet  or  1.308  cubic  yards. 

1,000  board  feet  of  sawn  lumber,  1  inch  and  more  thick,  correspond 
with    2.36    cubic    meters   of   sawn    lumber. 

A  product  of  one  cubic  meter  per  hectar  (2^2  acres)  equals  a  product 
of   14  cubic  feet  per  acre. 

One  gallon  equals  231  cubic  inches  in  liquid  measure,  or  268.8  cubic 
inches  in  dry  measure   (which  is  also  l/2  peck). 

One  liter  equals  1.0567  quarts;  one  cubic  foot  equals  74805  gallons 
or  28.3   liters. 

Logs  yielding  when  split  one  cord  of  wood,  will  yield,  when  sawn: 


For  log  diameter: 

Feet  board  measure: 

20" 
25" 
30" 
35" 
40" 

515' 
566' 
605' 
629' 
649' 

The  Forest  Reserve  Manual  adopts  2  cords  as  equivalent  to  1,000 
feet  b.  m.,  provided  that  the  wood  is  split  from  timber  10  inches  in  diam- 
eter and  over. 


12  Forest  Mensuration 

Table  Showing  Relative  Contents  of  Logs  Without  Bark. 


Log  diameter. 


i  cubic  foot  equals  ft.  b.  m.  Doyle 

i  cubic  meter  per  nectar  corre- 
sponds with  ft.  b.m.  Doyle  per 
acre : 

i  cubic  meter  of  log  yields  ft.  b. 
m.  Doyle: 

iooo  ft.  b.  m.  Doyle  equal  cubic 
ft: _. 

iooo  ft.  b.  m.  Doyle  equal  cubic 
meters !  .  .  . 

Artificial  cubic  feet  per  i  ft.  of  log 

No.  of  legal  N.  H.  feet  b.  m.  per 
i  ft  of  log : 

Ft.  b.  m.  Doyle  per  i  ft.  of  log. .  . 


44.8 

787.4 


4.12 


57-68 

86. 

145-5 

218. 

242.7 

161. 

6.87 
•4 

4- 

4- 

2-3 

9- 

7- 

15' 


6.2 


7-3 

102.2 

258.8 

1364 

3.86 
1.56 

156 
16. 


25 


8.09 

113.26 

285.7 
123.6 

3-5 
2-45 

24-5 
27-5 


30' 


8.64 


303 
116 


PARAGRAPH    XX. 


XYLOMETRIC    METHOD. 


The  so-called  "physical  methods,"  by  which  the  volume  of  a  (partic- 
ularly irregular)  piece  of  a  tree  may  be  accurately  found,  require  either 
the  submersion  of  the  piece  in  water  (xylometric  method)  or  the  weigh- 
ing of  the  piece  after  finding  its  specific  gravity  (hydrostatic  method, 
§XXL). 

The  xylometric  method  can  be  applied  in  three  ways,  thus : 

0.  Submerge  the  wood  in  a  graded  cylinder  partly  filled  with  water 
and  find  the  water  level  before  and  after  submersion. 

b.  Submerge  the  wood  in  a  barrel  partly  filled  with  water;  dip  out 
the  water  with  a  gallon  measure  until  the  water  is  as  low  as  it  was  before 
submersion.  The  number  of  gallons  dipped  out  equals  the  volume  of 
the  wood  submerged.     One  gallon  equals  231   cubic   inches. 

c.  Place  a  piece  of  wood  in  an  empty  barrel  of  known  contents ;  fill 
to  the  rim  with  water  by  the  gallon.  The  difference  between  the  known 
contents  and  the  number  of  gallons  required  gives  the  quantity  of  wood 
in  gallons. 

In  a,  b  and  c  it  is  necessary  to  use  wood  dry  on  the  outside,  to  leave 
the  wood  in  the  water  a  short  time  only,  and  to  stir  it  up  while  in  the 
water   so   as   to   remove   air   bubbles. 


PARAGRAPH  XXI. 

HYDROSTATIC      METHOD. 


The  hydrostatic  method  deals   with   specific   gravities.     Specific  gravity 
is   weight   of   an   object   divided   by   the   weight   of   an   equal    volume   of 


Forest  Mensuration 


13 


water.  In  the  metric  system,  it  equals  weight  in  kilograms  over  cube- 
decimeters  of  volume.  The  specific  gravity  is  found  by  weighing  a  given 
body,  and  then  weighing  it  again  immersed  in  water.  It  equals  weight 
outside  water  over  loss  of  weight  submerged  in  water.  The  division  of 
the  metric  weight  of  a  large  body  by  the  specfic  gravity  of  a  sample  piece 
yields  the  volume  of  the  body  in  cubic  decimeters. 

Since  wood  is  lighter  than  water,  usually,  a  piece  of  lead  must  be 
attached  to  the  wood  in  order  to  submerge  it.  There  must  be  ascer- 
tained : 

1.  The  absolute  weight  of  the  piece  of  lead,  H; 

2.  The  weight  of  the  same  piece  submerged   in  water,  h ; 

3.  The  absolute  weight  of  the  wood  and  of  the  lead,  G; 

4.  The  weight  of  wood  and  lead  submerged  in  water,  g. 

The  weight  of  the  wood  alone  is,  consequently,   (G — H). 
The  specific  gravity  of  the  wood  is 

G  — H 

S~(G-g)-(H-h) 

The  volume,  in  cubic  feet,  of  a  quantity  of  wood  weighing  n  pounds, 
and  having  the  specific  gravity  s,  is 

n        1  16n 

volume  =  —  X  —  = 

s        63        1000s 

The  figure  63  represents  the  weight  in  pounds  of  one  cubic  foot  of 
water. 

The  specific  gravity  of  wood  is  greatest  close  to  the  stump  and  in  the 
branches.  For  some  species  the  outer  layers  show  the  greatest  specific 
gravity;  for  others  the  inner  layers. 


Species. 

Spec,  gravity, 
air  dry. 

Weight  of  lumber  per 
1000  ft.  b.  m.  in  lbs. 

Weight  of  one 
cord  in  lbs. 

White  oak 

Beech 

Hard  maple .... 
Yellow  pine .... 

Spruce 

White  pine 

•75 
•7i 
.66 
•52 
•45 
•39 

3900 
3692 
3432 
2704 
2340 
2028 

3985 
3767 
35io 
2761 
2391 
2069 

Rules  to  convert  specific  gravity  into  weight  per  1,000  feet  board 
measure  or  into  weight  per  cord  read  as  follows : 

1.  Multiply  specific  gravity  by  5,200.  The  result  is  the  weight  of 
lumber  per  1,000  feet  board  measure  in  pounds. 

2.  Multiply  specific  gravity  by  percentage  of  solid  wood  contained  in 
a  stacked  pile;  then  multiply  the  product  by  8,050.  The  result  gives  the 
weight  per  cord  in  pounds. 


14  Forest  Mensuration 

FAllSXAPH  XXII. 

FACTORS    INFLUENCING   THE   SOLID   CONTENTS   OF   CORDWOOD. 

>v  The  solid  contents  of  wood  stacks  depend  on  the  size  and  the  form  of 

^r ^-       the  pieces  composing  them  and  on  the  method  of  piling.     The  solid  con- 

<v.  tents  of  a  cord  can  be  found  only  by  the  methods   described  in   Para- 

graphs XX.  and  XXI.  The  European  experiment  stations  have  collected 
"•^^V^^^^^data  to  that  end  on  a  very  large  scale,  and  have  established  the  following 
.-^p^  laws : 

^-^Vvaav^-^       a.     The  bigger  the  pieces  of  wood  in  a  stack,  the  larger  are  the  solid 
_vv^^^-~^-~~  contents  of  the  stack. 

X»~-  ^m^avtj-^j^ £.    The  longer  the  pieces  of  wood,  the  smaller  are  the  solid  contents 
of  the  stack. 


'  c.     Pieces  piled  parallel  and  tightly  greatly  increase  the  solid  contents 
of  the  stack. 

d.     During    the    drying    process,    hardwoods    shrink    approximately    by 
<s^J_^^^  12%,    and    soft    woods    by   9%.     The    shrinkage    is    partly    offset   by   the 
n  ^  cracking  of  wood. 

These  rules  are  important  in  the  pulp,  tanningwood  and  firewood  trade. 
PARAGRAPH  XXIII. 

REDUCING     FACTORS     FOR     CORDWOOD. 

The  countries  using  the  metric  system  pile  wood  in  space  cubic  meters. 
One  space  cubic  meter  equals  .274  cord.  The  pieces  contained  "therein 
are  3.28  feet  long.     For  such  conditions  the  following  figures  hold  good : 

a.  First  class  split  wood,  obtained  from  sound  pieces  12  inches  in 
diameter,  contains  per  cord  102.4  cubic  feet  of  solid  wood  (reducing  fac- 
tor 80%). 

b.  Composed  of  inferior  split  wood,  obtained  from  round  pieces  having 
a  diameter  of  6  inches,  a  cord  contains  96  cubic  feet  of  solid  wood  (re- 
ducing  factor  75%). 

c.  In  heavy,  round  branch  wood  (diameters  of  about  6^  inches) 
87  cubic  feet  of  solid  wood  are  found  in  a  cord  (reducing  factor  68%). 

d.  In  round  pieces  of  branch  wood,  4  inches  in  diameter,  yy  cubic 
feet  are  found  in  a  cord   (reducing  factor  60%). 

e.  In  faggots,  25  to  51  cubic  feet  make  a  cord  (reducing  factor  20% 
to  40%). 

The  percentages  for  broad  leafed  species  are  smaller  than  those  for 
conifers,  owing  to  the  latter's  straight  growth. 

At  Biltmore,  one  cord  of  8  foot  split  oak  contains  about  80  cubic  feet ; 
one  cord  of  kindling  finely  split  about  90  cubic  feet;  one  cord  of  blocks 
12  inches  long  about  100  cubic  feet  of  solid  wood. 


Forest  Mensuration  15 

In  the  sale  of  tannin  wood  it  is  well  to  sell  5  foot  sticks  finely  split 
rather  than  heavy  blocks  4  feet  long. 

In  the  sale  of  pulp  wood,  12  foot  sticks  yield  much  higher  returns  than 
4  foot  sticks,  if  sales  are  made  by  the  cord. 


PARAGRAPH    XXIV. 

LOCAL   PECULIARITIES   WITH   REFERENCE   TO   STACKED   WOOD. 

Tannin  and  pulp  wood  industries  sometimes  figure  at  a  cord  containing 
160  stacked  cubic  feet,  equal  to  \V\  ordinary  cords  of  128  stacked  cubic 
feet. 

After  Graves  (page  65),  a  cord  of  firewood  is  in  certain  sections  under- 
stood to  be  5  feet  long,  4  feet  high  and  6^2  feet  wide. 

Under  "a  cord  foot"  is  understood  a  stack  1  foot  by  4  feet  by  4  feet 
(%   cord   or    16   stacked   cubic    feet). 

Under  "a  cylindrical  foot"  is  understood  a  stacked  cubic  foot  equal 
to  1/128  cord.  The  number  of  such  feet  (a  misnomer  for  stacked  cubic 
feet)    in   a   stick   is 

d*Xl 
144 

(/  equals  length  of  stick  in  feet;  d  equals  its  diameter  in  inches). 

In  New  England,  a  cord  of  pulp  wood  is  sometimes  measured  by 
calipering  the  round  sticks  composing  it,  and  tables  are  constructed  to 
facilitate  calculation.     Proceed  as  follows : 

Ascertain  diameter  of  sticks  in  inches,  square  them  singly,  total  the 
results  and  divide  by  144.  Multiply  the  quotient  by  length  of  sticks  in 
feet  and  divide  by   128. 


PARAGRAPH   XXV. 

BARK. 

Bark  is  usually  sold  and  bought  by  the  cord.  The  tanneries,  however, 
instead  of  measuring  a  cord  of  128  cubic  feet,  apply  the  misnomer  "one 
cord"  to  a  weight  of  2,240  lbs.   (the  long  or  European  ton). 

Twelve  cords  of  bark  fill  one  common   (old)    freight  car. 

A  stack  of  bark  contains  from  30%  to  40%  solid  bark.  The  specific 
gravity  of  fresh  oak  bark  is  0.874;  dried,  it  is  0.764. 

The  bark  of  white  oak  has  been  found   (at  Biltmore),  to  comprise: 

In  trees  20  years  old,  55%  of  the  wood,  or  35%  of  the  whole  bole ; 
In  trees  60  years  old,  41%  of  the  wood  or  28%  of  the  whole  bole; 
In  trees  100  years  old,  29%  of  the  wood  or  22%  of  the  whole  bole ; 
In  trees  140  years  old,  21%  of  the  wood  or  17%  of  the  whole  bole. 


i6 


Forest  Mensuration 


Chestnut  oak  peeled  at  Biltmore  yields  the  following  results  per  tree, 
arranged  according  to  the  diameter  of  the  trees  4l/2  feet  above  ground: 


Diameter  of  tree 

Dry  Bark  in 

Kilogram  =  r^^  cord,  per  Tree. 

chest  high  in  inches. 

Minimum 

Average. 

Maximum. 

6 

5 

13 

27 

7 

6 

17 

36 

8 

8 

24 

48 

9 

12 

33 

61 

IO 

18 

45 

77 

ii 

26 

60 

95 

12 

37 

73 

114 

13 

50 

88 

135 

14 

65 

105 

158 

15 

81 

126 

180 

16 

98 

150 

204 

17 

116 

172 

234 

18 

136 

195 

266 

19 

159 

224 

3H 

20 

181 

250 

365 

21 

205 

275 

22 

230 

305 

23 

265 

336 

24 

275 

375 

If  the  percentage  of  bark  in  a  log  or  tree    (scaled  with  the  bark)    is 
p,  then  the  bark  percentage  in  ratio  to  the  solid  wood  alone  is : 

100  X  p 
100  — p 

According   to   thickness   of  bark   and    diameter   of   logs,   the    following 
percentages  can  be  given  for  the  ratio : 

bark 
bark  plus  timber 


Diameter  with 

Thickness  of  bark. 

bark — inches. 

\" 

1" 

1 4" 

2" 

10 

15 
20 

25 
30 

19% 

12% 

9% 

7% 

6% 

36% 
24% 
19% 
15% 
12% 

51% 
36% 
27% 
22% 
19% 

64% 
46  % 
36% 
29% 
24% 

Forest  Mensuration  17 


SECTION  II.— VOLUME  OF  STANDING  TREES. 
PARAGRAPH  XXVI. 

METHODS    OF    OBTAINING    THE    VOLUME    OF    STANDING    TREES. 

The  volume  of  standing  trees  may  be  ascertained 

By  estimating  it    (Par.   XXVII.)  ; 

By  measuring  heights  and  diameters   (Par.  XXVIII.)  ; 
By   the    form    factor    method,    which    combines    estimates    and    meas- 
urements   (Par.   XXIX.   f. f.). 

By  these  means  can  be  obtained  the  volume  of  the  bole  (from  roots  to 
top  bud),  or  the  volume  of  saw  timber  in  any  of  the  43  log  scales,  or 
the  volume  of  firewood  in  cords,  etc.,  or  the  total  volume,  including  brush 
and   roots. 

Under  "used  volume,"'  Circular  445  of  the  United  States  Bureau  of  For- 
estry understands  the  sum  of  the  volumes  of  logs  cut  from  a  tree ;  under 
"merchantable  volume"  the  total  volume  of  that  portion  of  the  tree  which 
is  merchantable   under  certain   conditions. 

PARAGRAPH  XXVII. 

HELPS    AND    HINTS    TO    FIND    THE    VOLUME    OF    STANDING    TREES. 

It  is  difficult  to  estimate  the  cubic  contents,  wood  contents  or  lumber 
contents  of  a  standing  tree.  In  the  case  of  estimates  in  board  feet,  the 
result  depends  on  the  exclusion  or  inclusion  of  crooked  and  defective 
pieces,  on  the  taper  of  the  bole,  on  the  soundness  of  the  heart,  and  on 
the  minimum  diameter  admissible  in  the  top  log.  Compare  end  of  Par- 
agraph   XXXII. 

Most  hazardous  is  the  volume  estimate  of  over-aged  trees,  especially 
in  the   case  of  hardwoods    (chestnut). 

The    following    helps    might    guide    the    novice : 

1.  The  volume  of  a  sound  tree  bole,  in  cubic  meters,  is  equal  to 

1000 
for  example,  diameter  (breast  high)  30  c.  m. ;  contents  0.9  cubic  meters. 

2.  The  contents  of  a  standing  tree,  in  cubic  feet,  are  about 

10 
for  example,  diameter    (breast  high),  25  inches;  contents    (from  butt  to 
tip),  125  cubic  feet. 

3.  The  number  of  feet  Doyle  in  a  tall  sound  tree  equal 

3 

— D2 
2 


1 8  Forest  Mensuration 

for  example,  diameter   (breast  high),  20  inches;  contents  600  feet  board 
measure. 

4.  The   contents  of  a  tree  in   feet   Doyle   approximate,   assuming  that 
the  bole  is  cut  into  16  foot  logs,  and  that  the  tree  tapers  2  inches  per  log : 

N  X  D  (D— 12) 

wherein  N  represents  the  number  of  logs  obtainable;  D  the  diameter  of 
the  butt  log  without  bark  at  breast  height. 

5.  The  cordwood  contained  in  a  sound  bole  is : 

D2 


X  C 
1000 


wherein    C   amounts    to : 


1.5  in  the  case  of  trees  8"   through ; 
2.0  in  the  case  of  trees    16"   through ; 
2.5   in  the  case  of  trees  24"   through. 


PARAGRAPH  XXVIII. 

SCIENTIFIC    METHODS    OF    ASCERTAINING    THE    CUBIC    CONTENTS    OF    STANDING 
TREES     BY     MERE     MEASUREMENT. 

The  cubic  volume  of  the  bole,  on  the  basis  of  diameter  measurement 
and  height  measurement,  in  the  case  of  a  standing  tree,  may  (with  the 
help  of  climbing  iron,  ladders,  camera  or  instruments  constructed  for 
the  purpose)    be  figured  out:  ►  . 

1.  According  to  the  formulas  of  Hossfeldt,  Riecke  and  Simony.  In 
this  case,  the  upper  diameters   must  be  measured  indirectly. 

2.  According  to  Huber's  and  Smalian's  formulas,  the  diameters  of 
equal  sections  of  the  trees  being  indirectly  measured. 

3.  According  to  Pressler's  formula,  which  is,  for  the  volume  of  the 
bole  lying  between  chest  height  and  top  bud,  2/3  of  sectional  area  "S" 
at  chest  height  times  "rectified"  height  of  bole.  The  rectified  height  "r" 
is  the  distance  of  chest  height  from  that  point  of  the  tree  bole  which 
has  l/2  of  the  chest  height  diameter  (from  the  "guide  point").  The 
equation  2/3  r  x  S  holds  good  for  paraboloid,  cone  and,  at  a  slight  mis- 
take,   for   the   neilloid. 

The  volume  of  that  part  of  the  tree  bole  which  lies  below  chest  height 
is  ascertained  (as  a  cylinder)  as  being  equal  to  sectional  area  chest  high 
times  4.5. 

Remark  :    4.3'   is  the  chest  height  usually   recognized  by  the  authors ; 
Pinchot  adopts  4.5'. 
The  Pressler  formula  does  not  hold  good  for  truncated  boles. 


Forest  Mensuration  19 

PARAGRAPH    XXIX. 

FORM    FACTOR    METHOD. 

The  form  factor  or  form  figure  method  relies  on  the  measurement  of 
the  sectional  area — usually  the  one  at  breast  height, — the  measurement 
or  the  estimation  of  the  total  height  and  the  estimation  of  the  form 
figure. 

The  form  factor  is  a  fraction  expressing  the  relation  between  the  actual 
contents  of  a  tree,  in  any  unit,  and  the  ideal  contents  which  a  tree  would 
have  if  it  were  carrying  its  girth  (like  a  cylinder)  up  to  the  top  bud 
undiminished. 

The  form  factor  may  be  given  in  reference  to  the  volume  of  the  entire 
tree,  inclusive  of  branches  in  cubic  feet ;  or  in  reference  to  the  volume 
of  the  bole  only ;  or  in  reference  to  the  merchantable  part  of  the  bole ; 
in  the  latter  case  either  in  feet  board  measure  or  in  standards  or  in  cords. 

Historic  Remarks  :  Some  of  the  older  authors  on  mensuration  saw  in 

the  cone  and  not  in  the  cylinder  the  ideal  form  of  the  tree,  basing  their 

s  X  h 
form  factors  on  the  ideal  volume . 


PARAGRAPH   XXX. 

KINDS    OF    FORM     FACTORS     MATHEMATICALLY. 

Scientifically  we  distinguish  between : 

1.  The  absolute  form  factors  which  have  reference  only  to  the  volume 
standing  above  chest  height.  They  can  be  readily  ascertained  with  the 
help    of    Pressler's    formula.     Generally    speaking,    V    equals    Sx  H  x  F. 

After  Pressler,  V  equals  S  x  2/3  x  r;   thus  *—  equals  F. 

H 
For  the  cone  the  absolute  form  factor  is  one-third ;  for  the  neilloid 
one-fourth ;  for  the  paraboloid  one-half,  whatever  the  height  of  the  tree 
may  be.  Hans  Rienicker,  the  author  of  these  form  factors,  finds  for 
trees  up  to  50  years  old  a  form  figure  of  35%  to  43%  (in  regular,  dense 
German  woods);  in  trees  50  to  100  years  old,  F  increases  up  to  50%; 
thereafter  occurs  a  slight  decrease  below  50%. 

2.  The  normal  form  factors  which  were  recommended  by  Smalian, 
Pressler  and  other  old-time  authors.  They  have  reference  to  the  entire 
volume  and  necessitate  the  measurement  of  the  diameter  at  a  given  frac- 
tion (usually  1/20)  of  the  total  height  of  the  tree.  Frequently,  in  case 
of  tall  trees,  the  point  of  measurement  cannot  be  reached  from  the  ground. 
The  bole  form  factor  for  diameters  measured  at  1/20  of  the  height  is : 
For  a  paraboloid,  0.526 ;  for  a  cone,  0.369 ;  for  a  neilloid,  0.292.  These 
form  factors,  like  the  absolute  form  factors,  are  independent  of  the  height. 

3.  The  so-called  "common  form  factors"  which  do  not  express,  as  a 
matter  of  fact,  the  form  of  the  tree,  since  they  do  not  bear  any  direct 
ratio   to   the   degree   of  the   tree   curve.     They   should   be   termed,    more 


20 


Forest  Mensuration 


properly,  "reducing  factors."  These  form  factors  alone  are  nowadays 
practically  used.  They  are  based  on  diameter  measurements,  chest  high, 
and  have  reference  not  merely  to  the  bole  of  the  tree,  but  as  well  to  any 
parts  of  the  bole,  to  root  and  branch  wood,  to  saw  logs,  etc.  These  form 
factors  depend  entirely  on  the  height.  If,  for  instance,  a  paraboloid  is 
one  rod  high,  the  form  factor  is  0.673 ;  and  if  it  is  8  rods  high,  the  form 
factor  is  0.517. 


PARAGRAPH    XXXI. 

KINDS     OF    COMMON     FORM     FACTORS     IN     EUROPEAN     PRACTICE. 

The  following  kinds  of  form  factors  may  be  distinguished : 

1.  Tree  form  factors.     The  tree  is  considered  as  bole  plus  branches. 

2.  Timber  form  factors.  The  term  timber,  in  Europe,  includes  all 
parts  of  the  tree  having  over  3  inches  diameter  at  the  small  end. 

3.  Bole  form  factors.  Bole  is  the  central  stem  from  soil  to  top  bud. 
For  America,  form  factors  would  be  of  great  value  ascertained  by  exact 
measurements  and  arranged  according  to  diameter,  height  and  smallest 
log  diameter  used. 

Tables  of  form  factors  may  be  constructed,  for  instance,  for  shortleaf 
pine,  on  the  basis  of  Olmsted's  working  plan,  pages   17-33. 

PlNUS    ECHINATA. 


Diameter. 

Merchantable  length 

Cubic  feet 

Form  fig. 

Contents 

of  bole. 

Ideal  cylinder. 

b.  m.  Doyle. 

16" 

36' 

50.3 

3-6 

*  180' 

18" 

47' 

83 

1 

3 

6 

300' 

20" 

5i' 

112 

1 

4 

0 

440' 

22" 

56' 

147 

8 

4 

0 

600' 

24" 

59' 

185 

3 

4 

2 

780' 

26" 

61' 

224 

9 

4 

4 

980' 

28" 

62' 

263 

1 

4 

5 

1 190' 

3o" 

62'  6" 

306 

7 

4 

6 

1420' 

32" 

63' 

35i 

8 

4 

7 

1680' 

34" 

63'  6" 

400 

3 

4 

8 

1930' 

36" 

64' 

457 

3 

4 

9 

2200' 

The  influence  of  age,  soil,  density  of  stand,  height,  diameter  and 
species  on  the  various  form  factors,  with  cubic  measure  as  a  basis,  has 
not  been   fully  ascertained. 

For  the  tree  form  factor,  the  most  important  influence,  in  the  case  of 
trees  less  than  150  years  old  and  raised  in  a  close  stand,  seems  to  be 
that  of  the  height  of  the  tree ;  with  increasing  height  the  tree  form  factor 
decreases — c.  g.,  for  Yellow  Pine : 

One  pole  high    93 

Two  poles  high 65 

Four   poles   high    53 

Six    poles    high    49 


Forest  Mensuration  21 

The  timber  form  factor,  based  on  cubic  measure  of  a  tree,  rises  with 
increasing  age  and  increasing  height  up  to  a  certain  point  (for  Yellow 
Pine  at  3  poles),  provided  that  the  term  timber  includes  all  stuff  over 
3  inches  in  diameter.  The  timber  form  factor  is  a  function  more  of 
the  diameter  than  of  the  height.  Timber  form  factors  of  Yellow  Pine 
are : 

Trees    1    pole   high    07 


Trees  2  poles  high 

Trees  3  poles  high 

Trees  4  poles  high 

Trees  7  poles  high 


The  timber  form  factor  in  shade  bearers  is  a  little  higher  than  that 
in  light  demanders  (within  an  age  limit  of  150  years,  for  trees  in  close 
stand). 

The  bole  form  factor  can  be  found,  in  fact,  only  for  species  forming 
a  straight  bole  free  from  large  branches  (hence  especially  for  conifers). 
The  bole  form  factors,  to  begin  with,  are  large ;  with  increasing  height, 
they  decrease  gradually  to  a  par  with  the  timber  form  factors — e.  g.,  for 
Yellow   Pine : 

1  pole   high 70  3  poles  high 49 

2  poles    high 55  4  poles  high 47 

7  poles  high 45 

European  common  form  factors  are  collected  by  thousands  of  measure- 
ments taken  in  a  large  variety  of  localities.  It  must  be  remembered  that 
a  form  factor  read  from  a  table  is  never  applicable  to  an  individual  tree, 
and  is  only  applicable  to  an  average  tree  amongst  thousands. 

For  trees  less  than  120  years  old,  the  branch  wood  (stuff  less  than  3 
inches  in  diameter)  comprises  from  15%  to  28%  of  the  entire  tree  vol- 
ume; this  figure,  in  the  case  of  broadleaved  species,  rises  from  25%  up 
to  33%.  For  trees  as  now  logged  in  America,  the  branchwood  percentage 
is    naturally    very    much    smaller. 

The    tree    form    factor    equals  stump  plus  bole  plus  branches 

ideal  cylinder 

The  timber  form   factor  equals  all  stuff  having  over  3"  diameter 

ideal  cylinder 

The  bole  form  factor  equals  bole  from  ground  to  tip 

ideal  cylinder 

By  form  height  is  meant  the  product  of  height  (total  height  of  tree) 
times  form  factor,  or  else  that  much  of  the  height  of  the  ideal  cylinder 
which  the  tree  volume,  poured  into  the  ideal  cylinder,  would  fill.  Since 
the  form  factor  on  the  whole  decreases  with  increasing  height,  the  form 
height  is  a  fairly  constant  quantity;  at  least  for  trees  of  merchantable 
size.  Hence  the  helps  and  hints  given  in  Paragraph  XXVII  (to  quickly 
find  the  volume  of  standing  trees  from  mere  diameter-measurement)  may 


22  Forest  Mensuration 

% 

lay  claim  to  correctness  in   many  cases.     For  instance :    The   cubic   con- 
tents of  a  tree  are  supposed  to  be  equal  to 

tt       D2  X  H  X  F 
X  ■ 

4  144 

After  Paragraph  XXVIL,  2,  these  contents  are  also 

2 
—X  D2 

10 

B- 

=  D2  X  78  X  H  X   F 

5 

288 
H  X  F  =  =37 

7.8 

As  a  matter  of  fact,  the  form  height  of  trees  I  foot  to  2  feet  in  diam- 
eter is  close  to  2>7-     And  for  such  trees  the  equation  holds  good. 

The  form  height  may  also  be  defined  as  "volume  (standards,  cords, 
bark,  etc.)   per  square  foot  of  sectional  area  chest-high." 

PARAGRAPH   XXXII. 

MEANS    FOR   EXACT    MENSURATION    OF    STANDING    TREES. 

The  means  used  to  find  the  exact  solid  volume  of  standing  trees  are 
instruments  for  measuring  the  total  height  of  the  merchantable  length 
of  a  tree ;  instruments  for  measuring  the  diameter  at  given  heights ;  fur- 
ther tables  based  on  scientific  research  and  experience,  or  tables  merely 
meant  to  facilitate  calculation.  Instruments  for  measuring  diameters  far 
above  ground  are  needed  for  the  use  of  the  formulas  given  by  Riecke, 
Hossfeldt,   Pressler,   etc. 

The  six  paragraphs  following  next  dwell  upon  these  topics. 

PARAGRAPH    XXXIII. 

MEASURING    THE    HEIGHT    OF    A    STANDING    TREE. 

The  height  of  a  tree  can  be  measured  by  comparing  its  shadow  with 
the  shadow  of  a  stick,  say  io  feet  long.  The  "Lumber  and  Log  Book" 
gives  another  old  method  (page  133)  of  height  measurement.  If  the 
observer  places  himself  in  such  a  way  that  a  small  pole  stands  between 
him  and  the  tree  at  a  distance  e,  and  if  he  marks  on  the  pole  two  points 
where  his  sight,  directed  towards  the  top  and  base  of  the  tree,  touches 
the  small  pole,  and  if  he  further  ascertains  the  distance  E  separating  him 
from  the  tree,  then  the  height  of  the  tree  H  equals 

E 

—  X   h 

e 

wherein  h  represents  the  number  of  feet  between  the  two  points  marked 
on  the  pole. 


Forest  Mensuration  23 

I 

Instruments  (hypsometers)  for  height  measuring  are  sold  in  many 
forms.  The  following  are  frequently  used:  Rudnicka's  instrument;  Press- 
or's "Measuring  Jack;"  Faustmann's  "Mirror  Hypsometer;"  Weise's  Tel- 
escope ;  Kcenig's  "Measuring  Board ;"  Brandis'  "Clinometer ;"  Klausner's 
instrument ;    Christen's    "Non    plus    ultra." 

Compare  Woodman's  Handbook,  pages  136  to  137,  for  staff  method; 
page  138  for  Faustmann's;  page  140  for  tangential  clinometer;  page  143 
for  mirror  clinometer. 

Christen's  stick  is  not  accurate  enough  for  the  measurement  of  trees 
over  100  feet  high.  It  does  not  require  the  measurement  of  distances.  Its 
form  is  improved  by  Pinchot. 

PARAGRAPH  XXXIV. 

FACTORS     INFLUENCING     THE     EXACTNESS     OF     HYPSOMETRICAL     OBSERVATIONS. 

The  best  results  are  obtained  if  the  distance  between  tree  and  observer 
equals  the  height  to  be  measured.  In  sighting  towards  the  spreading  top 
of  a  hardwood  tree,  the  observer  is  apt  to  overrate  the  height,  the  tip 
being  buried  in  the  spreading  crown.  The  line  of  sight  strikes  the  edge 
of  the  crown  instead  of  striking  the  apex  of  the  crown. 

Timber  cruisers  are  usually  satisfied  to  determine  the  number  of  logs 
obtainable  from  the  bole  instead  of  determining  the  length  of  the  bole. 
As  a  matter  of  fact,  where  the  tree  furnishes  saw  logs  only,  the  total 
height  of  the  tree  is  a  less  reliable  indicator  of  the  total  contents  than 
the  length  of  the  merchantable  bole. 

Instruments  like  Faustmann's,  Kcenig's  and  Pressler's  cannot  be  used 
in  windy  and  rainy  weather.  Dense  undergrowth  and  dense  cover  over- 
head render  exact  measurement  impossible. 

PARAGRAPH   XXXV. 

INDIRECT   MENSURATION   OF  DIAMETERS. 

The  following  instruments  are  used  to  measure  the  diameter  of  the  tree 
at  any  point  of  bole : 

a.  Winkler,  an  addition  to  Kcenig's  measuring  board. 

b.  Klausner. 

c.  An  ordinary  transit. 

d.  Wimmenauer's  telescope. 

PARAGRAPH    XXXVI. 

PRESSLER'S    TELESCOPE. 

Pressler's  telescope  is  used  to  find  the  "guidepoint"  and  the  "rectified 
height,"  as  defined  in  Paragraph  XXVIII.,  3.  The  diameter  chest-high 
is  taken  between  the  nails  at  the  end  of  the  instrument.  Then  the  tele- 
scope is  pulled  out  to  a  length  double  the  original,  divided  by  the  cosin 


24  Forest  Mensuration 

of  the  angle  found  between  the  horizon  and  the  probable  sight  to  the 
"guidepoint"  (at  which  the  observer  expects  to  find  one-half  the  diameter 
chest-high).  Thus,  actually,  the  instrument  merely  examines  the  correct- 
ness of  an  original  estimate. 

The  Pressler  telescope  can  be  used  for  finding  the  merchantable  length 
of  any  bole.  Merely  place  a  stick,  equal  in  length  to  twice  the  minimum 
diameter  permissible  in  a  merchantable  log,  at  the  foot  of  the  tree,  catch 
it  between  the  nail  points  and  proceed  as  described. 

PARAGRAPH  XXXVII. 

AUXILIARIES    FOR   CALCULATION. 

Auxiliaries   for  calculation  are : 

1.  Sectional  area  tables  (Schlich,  Vol.  III.);  engineering  books  like 
Haswell's;   Bulletin  20;  also  Green.) 

2.  Ideal  cylinder  tables    (Schlich  and  Bulletin  20). 

3.  Multiplication   tables   and   logarithm-tables. 

4.  Tables  showing  contents  of  logs  in  any  of  the  43  rules,  according 
to  length  and  diameter. 

PARAGRAPH  XXXVIII. 

TREE    VOLUME-TABLES. 

Tree  volume  tables  have  been  constructed  on  a  very  large  scale  for  the 
leading  species  in  the  old  country.  In  the  United  States,  the  Government 
is  now  beginning  to  make  such  tables.  The  tables  give  the  cubic,  dumber 
and  cord  wood  contents  of  trees,  according  to  species,  diameter  and  some- 
times according  to  total  height  and  merchantable  height  (number  of  logs). 

Bulletin  36  reprints  the  following  tree  volume  tables : 

A.     According  to  diameter  measure  merely. 

Page  92.     Adirondack   White   Pine,   volume   in   standards. 

Page  94.     Pennsylvania   Hemlock,  volume   in   feet,   b.   m.,   Scribner. 

Page  94.     Adirondack   Hemlock,   in   standards. 

Page  95.     Adirondack    Spruce   in   standards. 

Page  96.  Adirondack  Birch,  Beech,  Linden,  Sugar  Maple  in  Scribner, 
feet,   b.    m. 

Page  96.     Adirondack  Balsam,  in  standards. 

Page  97.     Adirondack  White  Cedar,  in  standards. 

Page  98.     Arkansas  Shortleaf  Pine,  in  feet,  b.  m.,  Doyle. 

Page  98.  Missouri  Ash,  Elm,  Maple,  Cypress,  Gum,  Oak,  Hickory, 
Poplar,   in  feet,  b.  m.,  Doyle. 

Page' 99.  Western  Yellow  Pine,  in  feet,  b.  m.,  Doyle  (Black  Hills),  dis- 
tinguishing between  the  volume  of  first  and  second  growth. 

Page  99.  Yellow  Poplar  in  Pisgah  Forest  in  feet,  b.  m.,  Doyle,  distin- 
guishing between  good,  average  and  poor  conditions  of 
growth. 


Forest  Mensuration  25 

All  tables,  except  Yellow  Poplar  tables,  are  based  on  the  measurement 
of  a  large  number  of  trees.  The  Yellow  Poplar  tables  are  based  on  stem 
analyses  of  a  small   number  of  trees. 

B.     According  to  measurement  of  height  and  diameter  combined. 

Page     93.     Wisconsin  White  Pine   (height  expressed  by  the  number  of 

logs  obtainable  from  merchantable  bole)  in  feet,  b.  m.,  Doyle. 
Page  103.     Adirondack   Spruce  expressed   in   feet,   b.   m.,   Scribner,  the 

total  height  of  trees  being  measured. 
Page  104.     The  same  in  cubic  feet. 
Page  105.     The  same  in  cords  for  pulp  wood. 
Page  106.     New  Hampshire  Spruce  in  feet,  b.  m.,  in  New  Hampshire 

cubic  feet  sanctioned  by  law. 
Pages   108  and   ill.     Adirondack  White   Pine  with  bark,   expressed   in 

cubic  feet. 
Page  no.     Adirondack  White   Pine  in   feet,  b.   m.,   Doyle. 

Monographic  investigation  into  the  growth  of  the  leading  American  spe- 
cies is  of  great  importance.  The  trees  of  virgin  forests  are  very  defective, 
however,  and  tree  tables  can  never  be  constructed  giving  the  contents  of 
defective  trees. 


SECTION  III.— VOLUME  OF  FORESTS. 
PARAGRAPH  XXXIX. 

SYNOPSIS    OF    METHODS    FOR   ASCERTAINING    THE    VOLUME    OF    FORESTS. 

The  methods  used  to  find  the  volumes  of  entire  forests,  of  forest  com- 
partments, tracts,  quarter  sections,  coves,  etc.,  are : 

1.  Estimating   (Par.   XL.). 

2.  Exact  calculation  after  measurements    (Par.  XLI.,   f.   f. ). 

3.  Combined  measuring  and  estimating    (Par.   IL.,   f.   f.). 

Obviously,  measuring  without  estimation  is  possible  only  in  forests  con- 
taining little   unsound  timber. 

PARAGRAPH   XL. 

ESTIMATION    OF    FOREST    VOLUME. 

In  primeval  woods,  where  a  few  assortments  only  are  salable  and  where 
stumpage  is  cheap,  the  estimation  of  stumpage  necessarily  takes  the  place 
of  the  measurement.  If  any  measurements  are  taken,  they  are  merely 
meant  to  back  the  estimation  of  the  cruiser.  The  more  defective  the  trees 
are,  the  more  preferable  is  judgment  and  local  long  experience  in  the  mill 
and  in  the  woods  on  the  side  of  the  cruiser  to  mere  measuring. 


26  Forest  Mensuration 

The  volume  of  a  wood  is  ascertained  by  cruisers'  estimates  in  the  fol- 
lowing ways : 

a.  By  estimating  the  number  of  trees  and  the  volume  of  the  average 

tree  with  due  allowance  for  defects. 

b.  By  counting  the  trees  and  estimating  the  volume  of  average  trees 

with  allowance  for  defects. 

c.  By  estimating  the  volume  of  each  tree  separately,  sounding  it  with 

an   axe,   when  necessary,   and  judging   its   soundness   from  all 
sides. 

The  above  methods  (a,  b,  c)  are  applied  either  to  sample  plots  or  to 
sample  strips  or  to  the  entire  area. 

A  blazing  hammer  is  often  used  to  prevent  duplication;  the  revolving 
numbering  hammer  might  be  used  in  case  of  scattering  trees,  so  as  to 
allow  of  control  of  the  estimates  by  the  owner,  his  forester  or  the  pros- 
pective purchaser  of  stumpage. 

In  irregular  forests — hardwood  forests  of  the  United  States — the  only 
safe  way  is  separate  estimating  of  each  individual  tree  after  careful  in- 
specting.    Incredible  errors  result  from  wholesale  and  rapid  estimates. 

In  the  case  of  even  aged  woods,  a  look  at  the  height  growth  and  a 
knowledge  of  the  age  gives  a  good  idea  of  the  forest's  volume.  Under 
very  poor  conditions  of  growth,  the  annual  timber  production  per  acre 
and  year  is  as  little  as  15  cubic  feet;  under  the  best  conditions  it  is  as 
much  as  250  cubic  feet  per  acre  and  year.  On  an  average  (on  absolute 
forest  soil),  50  cubic  feet  per  acre  and  year  may  be  considered  as  the 
production  of  healthy  and  densely  stocked  forests. 


PARAGRAPH  XLI. 

PRINCIPLES    UNDERLYING    THE    EXACT    MENSURATION    OF    FOREST    VOLUME. 

The  basis  of  any  exact  measurement  of  volume  is  formed  by  a  survey 
of  the  sectional  area,  combined  with  an  account  of  the  number  of  stems ; 
sectional  area  and  number  are  found  by  calipering  (valuation  survey). 
Whatever  rule  of  log  measurement  may  be  at  stake,  the  total  sectional 
area  of  the  forest  is  always  of  first  importance  for  a  survey  of  forest 
volume.  Next  in  importance  is  the  calipering  of  sample  trees,  followed 
by  an  exact  survey  of  their  volume.  The  ratio  r  existing  between  the 
volume  of  the  sample  trees  (expressed  in  any  unit  or  mixture  of  units) 
and  the  sectional  area  of  the  sample  trees  is  identical  with  the  form 
height  (compare  Par.  XXXII.,  towards  end)  of  the  sample  trees.  The 
form  height  of  sample  trees  properly  selected  is  the  form  height  of  the 
forest.  The  sample  trees  are  usually  cut  and  worked  up  into  logs,  cord- 
wood,  tannin  wood,  etc.,  for  the  purpose  of  volume  survey. 

V  v         f.  h.  s. 

—  —  _  =  and         V  —  S.  f.  h 

S  s  s 


Forest  Mensuration 


27 


If  the  trees  of  the  forest  are  defective,  the  sample  trees  should  exhibit 
average   defects. 


PARAGRAPH    XLII. 

FIELD    WORK    FOR    EXACT    VALUATION    SURVEYS. 

The  valuation  survey  requires : 

1.  Calipering  of  all  trees;  the  diameter  is  taken  in  inches  or  in  multi- 
ples of  inches.  Each  species  and  each  height  class  or  age  class  are  or 
may  be  taken  separately. 

2.  Entering  the  takings  on  tally  sheets,  arranged  as  follows : 


Diameter. 

Spruce. 

Beech. 

Height  classes. 

Height  classes. 

I 

II 

I 

II 

10" 

n" 

12" 

13" 
etc. 

The  larger  the  trees  are,  the  bigger  is  the  permissible  interval  of 
calipering.  If  trees  average  two  feet  in  diameter,  an  interval  of  3  inches 
is  permissible,  provided  that  a  large  number  of  trees  are  calipered. 

It  is  a  strange  fact  that  the  diameter  measured  from  east  to  west  is 
larger  on  the  whole  than  the  diameter  from  north  to  south. 


PARAGRAPH    XLIII. 


BASAL    ASSUMPTIONS. 


The  only  assumption  made  in  calculating  the  volume  of  the  forest  after 
Paragraph  XLI.  is  that  the  form  height  of  the  sample  trees  equals  the 
form  height  of  the  forest.  No  other  estimate  or  assumption  is  being 
made.  This  premise  is  much  safer  than  the  assumption  that  the  volume 
of  the  forest  bears  the  same  ratio  to  the  volume  of  the  sample  trees 
which  the  number  of  trees  in  the  forest  bears  to  the  number  of  the  sample 
trees.  More  unsafe  is  the  assumption  that  the  volumes  of  forest  and 
sample  trees  bear  the  ratio  of  the  acreage  occupied  by  the  forest  on  the 
one  hand  and  by  the  sample  trees  on  the  other  hand. 


28 


Forest  Mensuration 


PARAGRAPH  XLIV. 


SELECTION     OF     SAMPLE     TREES. 


Sample  trees  are  selected  either  irregularly  or  after  a  regular  plan.  In 
the  latter  case,  it  is  best  to  distribute  them  equally  among  the  diameter 
classes  composing  the  forest  (Draudt-Urich  method  and  Robert  Hartig 
method),  instead  of  selecting  sample  trees  of  average  diameter. 

It  is  more  important  that  the  sample  trees  should  have  proper  average 
class-form  height  (and  average  defects)  than  that  they  should  have  exact 
average   class-diameters. 

PARAGRAPH   XLV. 

DRAUDT-URICH      METHOD. 

The  Draudt-Urich  method  is  in  common  use  abroad  for  measuring 
the  forest.  The  trees  of  the  forest  are  divided  into  a  number  of  classes 
(usually  five).  Each  class  contains  an  equal  number  of  trees,  class  I 
containing  the  largest  and  class  5  the  smallest  trees.  In  each  class  an 
equal  number  of  sample  trees,  having  about  the  average  diameter  of  the 
class,  are  felled  and  worked  up  into  logs,  cordwood,  ties,  poles,  etc.  The 
form  height  of  all  sample  trees  is  obtained  as  the  quotient  of  their  volume 
(in  any  unit  or  mixture  of  units)  divided  by  their  sectional  area.  Mul- 
tiplying the  sectional  area  of  the  forest  with  this  form  height,  the  exact 
volume  of  the  entire  forest  and  its  composition  (logs,  poles,  cords,  etc.) 
are  given  by  one  operation. 

Sample  trees  of  the  average  diameter  of  a  class  are  found  by  dividing 
the  sectional  area  of  the  entire  class  by  the  number  of  trees  per  class.  It 
is  wrong  to  find  the  average  diameter  by  dividing  the  sum  total  of  the 
diameters  by  the  number  of  trees. 


Diameter 
Breast  High. 

Number 

of 
Trees. 

Diameter 
Classes 
of  Trees. 

Number 

of  Sample 

Trees. 

Average  Diam- 
eter of  Sample 
Trees. 

40" 
35" 
30" 

25"        | 
20" 

15"        j 

( 

10"        \ 

1 

310 

240 

506 

1226 

I 

1 1 

29" 

9 
1040 

1233 

II 

1 1 

17" 

1847 
435 

III 

1 1 

14" 

2282 

IV 

1 1 

10" 

! 
1 

2282 

V 

1 1 

10" 

Forest  Mensuration  29 

The  advantages   of  the   Draudt-Urich   method  are : 

r.     All  sample  trees  can  be  worked  up  in  a  bunch. 

2.  Not  only  the  entire  volume  but  as  well  the  different  grades  of  tim- 
ber, fuel,  ties,  etc.,  composing  the  volume  are  found  by  one  operation. 

A  large  number  of  sample  trees  are,  however,  required,  and,  since  the 
volumes  of  the  various  classes  are  unequal,  a  negative  mistake  made  in 
establishing  the  volume  of  one  class  is  not  apt  to  be  counter-balanced  by 
a  positive  mistake  made  in  finding  the  volume  of  another  class. 

PARAGRAPH    XLVI. 

ROBERT     HARTIG     METHOD. 

Robert  Hartig's  method  forms  tree  classes  containing  equal  sectional 
areas— not  equal  numbers  of  trees.  An  equal  number  of  sample  trees  is 
cut  in  each  class  and  worked  up  separately  for  each  class.  The  volume 
of  the  forest  is  also  obtained  separately  for  each  class.  Otherwise,  the 
manner  of  proceeding  is  identical  with  that  of  Paragraph  XLV. 

Preferable  it  would  seem  to  cut  in  each  class  a  number  of  sample  trees 
having,  in  the  aggregate,  the  same  sectional  area.  This  scheme,  how- 
ever, would  represent  the  big-diameter  class  by  an  absurdly  small  num- 
ber of  samples. 

PARAGRAPH    XLVII. 

AVERAGE    SAMPLE   TREE    METHOD. 

If  average  trees  of  the  entire  rorest  are  taken  as  samples,  then  the 
volume  of  the  forest  is  obtained  with  smaller  accuracy. 

The  proportion  which  the  different  assortments  of  timber,  wood,  bark, 
etc.,  form  in  the  entire  output  is  not  clearly  shown  by  such  sampling. 

In  a  normal,  even-aged  wood  the  tree  of  average  cubic  volume  is  found 
by  deducting  40%  from  the  total  sectional  area,  beginning  with  the  de- 
duction at  the  biggest  end.  The  largest  tree  then  left  is,  or  happens  to 
be,  the  average  tree  of  the  wood. 

PARAGRAPH    XLVIII. 

EXACT    MENSURATION     WITHOUT    CUTTING    SAMPLE    TREES. 

Frequently  the  cutting  of  sample  trees  for  the  purpose  of  a  valuation 
survey  is  not  feasible.  The  volume  of  the  forest  in  cubic  feet — but  not 
the  assortments  composing  the  volume — may  then  be  ascertained  as  fol- 
lows : 

a.  Take  the  total  sectional  area  of  the  forest  according  to  diameters 
and  species  and,  if  necessary,  according  to  height  classes. 

b.  Ascertain  the  bole  volume  of  some  available  trees  with  the  help  of 
Pressler's  tube  or  by  indirect  measurement  of  heights  and  diameters. 


30  Forest  Mensuration 

c.  Proceed  as  indicated  in  the  last  three  paragraphs,  keeping  in  mind, 
however,  that  only  the  cubic  volume  of  the  boles  is  thus  obtainable.  The 
branch-wood-percentage  or  the  timber-percentage  of  the  bole  must  be 
estimated. 

The  Hartig  method  (Paragraph  XLVI.)  might  be  combined  with  the 
use  of  Pressler's  telescope,  and  the  bole  volume  of  a  wood  above  breast 
height  might  be  ascertained  as  2/3  of  the  total  sectional  area  of  the 
forest,  multiplied  by  the  arithmetical  mean  of  the  rectified  heights  of 
the   sample   trees    representing   the   various    diameter   classes. 

2  S  (rt  +  r2  +  r-3  +  r4  +  r„) 
V  =         X  

3  5 

The  bole  volume  below  breast  height  in  cubic  feet  is  equal  to  the 
sectional  area  of  the  wood  times  4J/2. 

PARAGRAPH  XLIX. 

COMBINED    MEASURING   AND   ESTIMATING. 

If  measuring  and  estimating  are  combined,  the  following  typical  meth- 
ods may  be  used  to  ascertain  the  volume  of  woods : 

1.  The   form   factor   method    (Paragraph   L.). 

2.  The  form  height  method    (Paragraph  LI.). 

3.  The  volume  table  method    (Paragraph  LIL). 

4.  The  yield  table  method    (Paragraph  LIIL). 

These  methods  might  be  used  in  connection  with  the  so-called  "dis- 
tance figure"  of  Paragraph  LIV. 

In  applying  these  methods,  one  or  the  other  of  the  three  factors  of 
volume  (sectional  area,  height  and  form  factor)  are  obtained  by  estima- 
tion. 

The  paragraphs  following  Paragraph  LVIII.  give  a  number  of  methods 
practically  used  and  also  based  on  combined  measuring  and  estimating. 

PARAGRAPH    L. 

FORM    FACTOR    METHOD. 

The  form  factor  method  ascertains  the  sectional  area  by  calipering, 
according  to  species,  and,  if  necessary,  according  to  height  classes.  The 
average  height  of  the  wood  (by  species,  classes)  is  obtained  by  actual 
hypsometric  measurement.  The  form  factor  is  read  from  local  form 
factor  tables. 

The  average  height  is  obtained — not  as  the  arithmetic  mean  of  a  num- 
ber of  heights  measured,  but  much  more — correctly  from  the  ratio  exist- 
ing between  the  sum  total  of  the  ideal  cylinders  and  the  sum  total  of 
the  sectional  areas  of  the  trees  hypsometrically  measured.  The  form 
factors  appearing  in  form  factor  tables  must  be  averages  obtained  by 
many  hundreds  of  local  measurements. 


Forest  Mensuration  31 

Mistakes  amounting  to  up  to  25%  in  the  sum  total  of  the  volume 
obtained  by  the  form  factor  method  are  not  impossible,  since  average 
form  factors  appearing  from  a  form  factor  table  are  often  at  variance 
with   the  actual   form   factor. 

Form  factor  tables  for  American  "second  growth"  are  still  lacking.  In 
primeval  woods  the  form  factor  method  seems  out  of  place. 


PARAGRAPH    LI. 

FORM    HEIGHT    METHOD. 

The  form  heights  of  merchantable  trees  are,  generally  speaking,  sub- 
ject to  only  small  variations.  Those,  e.  g.,  for  Adirondack  White  Pine 
scaling  from  18"  to  36"  in  diameter  breast-high  are  (for  standard  rule) 
close  to   1.25. 

Multiplying  the  sectional  area  of  a  White  Pine  woodlot  (say  100  square 
feet)  by  the  form  height  previously  obtained  through  official  measure- 
ments (like  those  by  T.  H.  Sherrard),  the  volume  of  the  woodlot — in 
the  present  example  about  125  standards — is  easily  obtained. 

Form  height  tables  based  on  feet  b.  m.,  Doyle,  are  not  as  simple  as 
those  based  on  the  standard  rules  and  cubic  foot  rules,  owing  to  the 
mathematical  inaccurary  of  Doyle's  rule,  which  causes  the  form  heights 
to  be  pre-eminently  dependent  on  the  diameters. 

Form  height  tables  should  be  constructed  for  the  leading  merchantable 
species  in  the  United  States.  Of  course,  such  tables  are  more  readily 
applicable  to  second  growth  than  to  first  growth. 

The  form  height  tables  should  exhibit  the  number  of  standards,  cords, 
ties,  etc.,  obtainable  per  square  foot  of  sectional  area  in  each  diameter 
class.  In  case  of  defective  trees,  proper  allowance  must  be  made  for 
defects — rather  a  hazardous  risk  in  primeval  hardwoods. 


PARAGRAPH   LII. 

VOLUME     TABLE      METHOD.      \^_l-3--<S    <Fv   WaX- /0^-^i_vj '       V 

In  Paragraph  XXXVIII.  a  number  of  volume  tables  have  been  enum- 
erated, from  which  the  volume  of  trees  of  given  species  and  diameter 
(and  height)    can  be  readily  read. 

A  valuation  survey  of  the  forest  (or  of  a  woodlot  or  of  a  sample  plot) 
yields  the  diameters  of  the  trees  stocking  thereon.  The  number  of 
trees  found  for  each  diameter  class  is  multiplied  by  the  contents  of  a 
tree  of  that  diameter  appearing  from  the  volume  table.  The  sum  total 
of  the  multiples  is  the  sum  total  of  the  volume  of  the  forest. 


32 


Forest  Mensuration 
Sample. 


u 
+J 

B 

Yellow  Pine. 

Hickory. 

Oak. 

03 

s 

No. 
trees. 

Average 
volume. 

Total 
volume. 

No. 
trees. 

Average 
volume. 

Total 
volume. 

No. 
trees. 

Average 
volume. 

Total 
volume. 

12 

15 

18 

21 

24 

27 

30 

33 
36 

30 
42 
17 
36 
33 
20 
10 
1 
1 

60 

I20 

300 

520 

780 

1080 

1420 

1800 

2200 

I  .800 

5.040 

5.IOO 

18.720 

25.740 
2  I  . 600 
14. 200 

1  .  800 

2  .  200 

7 

9 

18 

5 

12 

6 

3 

140 
240 
370 
500 
660 
840 
1050 

980 
2160 
6600 
2500 
7920 
5040 
3150 

14 
5 
23 
22 
22 

7 
10 

5 

5 

160 

200 

350 

520 

730 

940 

1 1  50 

1400 

1800 

I  .400 

I  .OOO 

8.050 

1 1 . 440 

i 6 . 060 

6.580 

1 1 . 500 

7  .000 

9.000 

Totals . 

96 . 200 

28.350 

72.030 

Grand  total 196.580'  B.  M. 


The  volumes  of  the  column  "Average  Volume"  are  taken  from  tables 
published  by  the  Bureau   of  Forestry. 


PARAGRAPH    LIII. 


YIELD    TABLE    METHOD.  r>sv 


^XXV.    ^M^x 


^ 


All  over  Europe  local  yield  tables  are  used  to  quickly  ascertain  the 
volume  of  pure,  sound,  even  aged  woods.  For  America,  such  yield  tables 
— normal  local  yield  tables — exist  only  in  the  white  pine  tables  given  in 
Pinchot  and   Graves'   pamphlet,   "The   White   Pine." 

The  method  of  construction  of  yield  tables  appears,  from  Paragraph 
XCII.  and  following. 

Under  yield  tables  are  understood  "acre-volume-tables,"  whilst  under 
volume  tables   are   understood   "tree-yield-tables." 

Normal  yield  tables  specify  the  age  of  even  aged  and  pure  woods,  the 
height  of  such  woods  and  the  volume  (by  assortment)  of  such  woods, 
according  to  the  productiveness  of  the  soil.  An  indication  for  the  latter 
is  found  in  the  height  growth. 

Such  yield  tables  hold  good  only  for  woodlots  normally  stocked.  A 
woodlot  is  normally  stocked  "when  all  local  factors  of  wood  production 
have  pronounced  themselves  unhampered  in  the  annual  production  of 
fibre."  Normal  woods,  even  of  small  extent,  are  extremely  rare.  In  Ger- 
many the  average  wood  lacks  25%  of  being  normal.  Since  the  normal 
yield  tables  give  the  yield  for  normal  conditions  only,  a  deduction  must 
be  made  from  the  volume  indicated  by  the  yield  table  when  applied  to 
a  given  woodlot,  according  to  the  abnormality  of  the  same. 

Proceed  as  follows : 


Forest  Mensuration  33 

Ascertain  age  and  average  height  of  the  trees ;  find  the  yield  table 
which  gives  a  similar  height  for  the  same  age;  reduce  the  volume  indi- 
cated by  this  yield  table  and  for  this  age,  by  estimating  the  deficiency  of 
the  growing  stock. 

Obviously,  there  is  much  room  for  guessing,  since  neither  height  nor 
form  figure  nor  sectional  area  in  woodlots  abnormally  stocked  can  lay 
claim  to  normality. 

Schuberg,  denying  a  truism  otherwise  generally  acknowledged,  claims 
that  the  height  alone  does  not  indicate  the  productiveness  of  the  soil. 

At  present,  normal  yield  tables  are  of  little  use  in  American  forestry. 


PARAGRAPH    LIV. 

DISTANCE     FIGURE. 

Under  "distance  figure,"  an  invention  of  Koenig's,  is  understood  the 
quotient  a  formed  by  the  side  /  of  the  average  growing  space  of  a  tree 
(considered  as  a  square)   and  by  the  diameter  of  the  average  stem  d. 

1 
a   =  — 

d 

The  average  distance  from  tree  to  tree  and  the  average  diameter  of  a 
number  of  trees  is  obtained  by  a  number  of  measurements  in  the  forest. 
If  the  area  of  the  forest  is  F  square  feet,  then  the  sectional  area  of  the 
forest  is 

7T  F 

=  —  X   —  square  feet 
4  a2 

The  actual  test  proves  the  fallacy  of  Koenig's  assumptions.  The  ex- 
planation lies  in  the  fact  that  the  average  diameter  of  a  wood  is  not  the 
arithmetical  mean  of  the  diameters  composing  it.  Further,  the  growing 
space  of  a   tree   is  not   a   square. 

The  actual  growing  space  per  tree  can  be  correctly  ascertained  by  laying 
a  sample  strip  through  the  forest,  counting  at  the  same  time  the  trees 
within  the  strip.  The  sectional  area  of  the  forest  is  obtainable,  however, 
without  greater  trouble  and  with  much  greater  accuracy,  from  the  pro- 
duct calipered  sectional  area  of  trees  in  the  sample  strip  times  area  of  the 
forest  over  area  of  the  sample  strip. 

On  an  acre  of  average  soil,  there  is  on  an  average  room  for  the  fol- 
lowing numbers  of  healthy  trees,  according  to  age : 


At  20  years  1,600  specimens. 
At  50  years  600  specimens. 
At  100  years  240  specimens. 
At  150  years      150  specimens. 


34 


Forest  Mensuration 


PARAGRAPH    LV. 
algon's  universal  volume  tables. 

So-called  "universal  volume  tables"  have  been  constructed  by  H.  Algon, 
a  Frenchman.  For  a  description  of  these  tables  see  "Indian  Forester" 
of  July,    1902. 

The  volumes  given  for  each  diameter  of  trees,  whatever  the  species  be, 
are  presented  on  a  number  of  tables  as  follows : 


Volume  in  Cubic  Feet. 

Diameter. 

Tabk 

:  1.        Table  5. 

Table  10. 

Table  15. 

Table  20. 

6" 

2 

3- 

4- 

6. 

8. 

9" 

5 

8 

10 

16. 

18 

12" 

9 

15 

21 

27. 

33 

15" 

19 

28 

39 

50. 

61 

18" 

27 

39 

59 

69. 

84 

21" 

43 

60 

83 

109. 

128 

24" 

54 

78 

108 

138. 

168 

27" 

72 

107 

147 

188. 

228 

30" 

87 

129 

177 

228. 

276 

33" 

in 

163 

221 

288. 

349 

36" 

129 

189 

258 

333- 

405 

The  tables  are  used  as  follows : 

1.  Caliper  the  entire  forest  according  to  diameters  and  species. 

2.  Measure  a  number  of  type  trees,  selected  at  random,  after  felling 
them. 

3.  Find  that  volume  table  amongst  the  20  tables  given  which  best  cor- 
responds with  the  diameters  and  volumes  of  the  type  trees.  Apply  the 
volume  table,  which  is  found  to  be  the  proper  one,  to  all  diameter  classes 
calipered   in   the  woods. 

Objections  to  the  method  are: 

a.  The  danger  of  mistakes  is  very  great.  In  an  absolutely  even  aged 
wood,  one  tree  of  15  inches  diameter  may  easily  show  50%  more  volume 
than  another  tree  of  the  same  diameter,  the  latter  being  more  tapering 
and  shorter. 

b.  In  an  uneven  aged  wood  the  tables  are  necessarily  wrong  because 
the  form  height  is  a  function  of  age  as  well  as  of  height  and  diameter. 

c.  The  method  does  not  give  any  idea  of  the  proportion  of  logs,  fuel, 
bark,  etc. 

Algon  calls  these  tables  "universal"  assuming  that  they  hold  good  for 
all  species  of  the  universe. 


Forest  Mensuration  35 

PARAGRAPH   LVI. 

schenck's  graphic   method. 

This  method,  as  well,  can  be  used  only  for  sound  woods.  No  calcu- 
lation  is   required.     The  procedure   is : 

1.  Caliper  the  whole  wood. 

2.  Cut  sample  or  type  trees  of  small,  big  and  average  diameters,  find 
the  contents  of  each  tree  separately,  together  with  the  composition  of 
contents  as  logs,   fuel  and  bark. 

3.  On  a  piece  of  cross  section  paper,  use  as  many  units  along  a  hori- 
zontal line  as  there  are  trees  (or  tens  or  hundreds  of  trees)  calipered. 

4.  Mark  the  unit  which  each  sample  tree,  according  to  its  diameter, 
would  occupy  if  the  biggest  tree  were  placed  to  the  right  and  the  smallest 
to  the  left  of  the  horizontal   line. 

5.  Enter  over  the  marked  units  the  volume  of  the  type  trees  (accord- 
ing to  the  composing  factors,  if  required)  in  square  units.  A  square  unit 
might  correspond  with  ten  feet  board  measure,  or  with  1/100  of  a  cord, 
etc. 

6.  Draw  a  line  joining  the  ends  of  the  columns,  adjusting  it  by  an 
average  curve. 

7.  Measure  the  space  (in  square  units)  between  the  curve  and  the 
horizontal  line  with  the  help  of  a  planimeter;  the  number  of  square  units 
giving  directly  the  number  of  feet  Doyle,  or  of  cords,  etc. 

If  there  are  several  assortments  of  volumes,  several  curves  must  be 
drawn.  This  method  allows  of  separating  the  volumes  of  trees  allotted 
to  the  several  diameter  classes.  Mathematical  errors  are,  practically, 
excluded. 

PARAGRAPH   LVII. 

FACTORS   GOVERNING  THE   SELECTION   OF   A   METHOD   OF   VALUATION   SURVEY. 

In  the  case  of  a  valuation  survey  ("stock  taking")  in  the  woods,  the 
following  points  must  be  considered  : 

a.  The  degree  of  exactness  required,  which  depends  on  the  purpose 
at  stake  {c.  g.,  scientific  investigations,  or  preparation  for  logging,  or 
taxation). 

b.  The  regularity,  uniformity  and  soundness  of  the  growing  stock. 

c.  The  minimum  diameter  of  logs ;  assortments ;  marketability  of  spe- 
cies. 

d.  The  possibility  of  cutting  sample  trees. 

e.  The  expense  permissible. 

The  question  usually  arises  whether  the  entire  forest  or  sample  plots 
only  must  be  surveyed.  The  answer  depends  on  the  configuration  of  the 
ground,  uniformity  of  the  growing  stock  as  to  size,  age,  species  and 
quality  of  its  components ;  further  on  the  value  of  stumpage,  on  the  accu- 
racy required,  on  the  available  time  and  on  the  available  funds. 


36  Forest  Mensuration 

The  following  METHODS  OF  VALUATION  SURVEYS  might  be 
distinguished : 

I.     Cutting  sample  trees. 

a.  Sample    trees    selected    for   about   five    diameter    classes,    each 

class  containing  about  one-fifth  of  the  number  of  trees  pres- 
ent  (Draudt-Urich  method). 

b.  Sample   trees    selected    for    about    five    diameter    classes,    each 

class  containing  about  one-fifth  of  the  sectional  area  of  all 
trees  present    (Robert  Hartig  method). 

c.  Sample  trees   selected  as  average-diameter-trees  of  the  entire 

forest   (Old  Bureau  method). 

d.  Sample  trees  selected  at  random — c.  g.,  from  dead  and  down 

trees    (C.    A.    S.    method — applied    in    the    Balsams;    Algon 
Universal  tables;   Graphic  method). 

e.  Stem  analysis,  together  wTith  investigations  as  to  thickness  of 

bark. 

II.     Without    cutting   sample    trees. 

a.  Measuring  height  and  diameter  and  estimating  form  figure  of 

sample  trees. 

b.  Measuring   rectified   heights   and   diameters. 

c.  Measuring  merely  diameters  and  estimating  form  heights. 

d.  Photographing  sample  trees,  having  a  scale — say  a  sti^k  6  feet 

long — on   the   picture. 

III.     With  the  help  of  volume  tables. 
IV.     With   the  help   of  yield  tables. 

PARAGRAPH    LVIII. 

FACTORS    INFLUENCING    THE    SELECTION    OF    SAMPLE    PLOTS. 

If  sample  plots  are  taken,  there  must  be  determined: 

a.  The  number,   situation   and   distribution  of  the   sample   plots. 

b.  The  absolute  and  relative  size  of  the  sample  plots.  The  Bureau  of 
Forestry  prescribes  sample  plots  equalling  from  I  to  4lA%  of  the  forest. 
The  "Forest  Reserve  Manual"  prescribes  5%  or  more. 

c.  The  form  of  the  sample  plots  and  the  manner  by  which  the  size  of 
the   sample   plot   is   ascertained. 

In  Europe  an  ordinary  workman  calipers,  on  an  average,  5,000  trees 
(in  maximo  12,000  trees)  per  day.  In  Pisgah  Forest  500  trees  is  a  good 
day's  work  for  one  estimator  and  one  helper. 


Forest  Mensuration  37 

•     PARAGRAPH    LIX. 

SIR    DIETRICH    BRANDIS'    METHOD. 

The  Brandis  method  is  indicated  where  the  object  at  stake  consists  in 
a  rapid  survey  of  the  stumpage  on  large  tracts,  like  the  vast  Teak  and 
Bamboo   forests  of  upper   Burmah. 

Traversing  existing  trails  of  known  length  on  horseback,  the  estimator 
records  the  diameter  of  each  tree  within  a  given  distance  (say  200  yards) 
on   either  side  of  the   trail. 

The  widths  of  the  strips  traversed  multiplied  by  the  length  of  the  trail 
yields  the  area  of  the  sample  plot.  The  number  of  the  trees  of  the 
various  diameters  found  on  the  sample  strip  appears  from  the  records. 


PARAGRAPH    LX. 

PIXCHOT-GRAVES     METHOD     ADOPTED     ON     DR.     WEBB'S     ESTATE. 

1.  Sample  acres,  measuring  4  x  40  poles,  are  irregularly  laid  into 
swamps,  hardwood  slopes  and  spruce  slopes.  The  sum  total  of  the  sam- 
ple acres  is  3^%  of  the  total  acreage. 

2.  The  length  of  a  sample  acre  is  actually  chained  off,  whilst  the  width 
is  ascertained  (two  poles  to  the  left  and  two  poles  to  the  right  of  the 
chain)    by   tape,   by  pacing  and  by  estimating. 

3.  The  sites  of  the  sample  acres  are  not  marked  on  maps. 

4.  All  trees  on  the  sample  acres  are  calipered ;  a  number  of  heights 
are  taken  on  each  sample  acre;  for  each  sample  acre  the  average  diam- 
eter, the  average  height  and  the  number  of  trees  are  ascertained. 

5.  From  these  averages  is  deduced,  for  all  sample  acres,  the  average 
diameter,  the  average  height  and  the  number  of  trees.  All  these  data, 
of  course,  must  be  given  for  the  various  species  separately. 

6.  From  volume  tables  previously  constructed  the  volume  of  the  trees 
having  average  height  and  average  diameter  is  obtained  and  is  multiplied 
by  the   average  number   of  trees. 

7.  This  multiplication  yields  the  volume  of  the  average  sample  acre. 
Objections  to  this  method  of  valuation  survey  are: 

a.  The    tree    of   average   diameter   has    neither   average   volume   nor 

average  height. 

b.  The  average  diameter  should  be  obtained  from  the  fraction  "total 

sectional  area  over  number  of  trees."  It  cannot  be  obtained 
correctly  from  the  fraction  "sum  total  of  diameters  over  num- 
ber of  trees."     Similar  objections  hold  good  for  average  height. 

c.  Guessing  at  the  width  of  a  strip,  in  dense  growth,  is  rather  risky. 


38  Forest  Mensuration 

Remark  :  Bulletin  36,  page  125,  states  that  volumes  are  now  computed 
by  the  Bureau  either  by  averaging  the  volumes  found  for  the  sample 
acres,  thus  obtaining  the  volume  of  a  model  acre  as 

n 

(wherein  n  equals  the  number  of  sample  acres)  ;  or  by  summing  up  all 
trees  of  each  diameter  class,  by  dividing  each  sum  by  the  number  of  sam- 
ple acres,  and  by  thus  finding  for  a  model  acre  the  average  number  of 
trees  for  each  diameter  class.  In  both  cases  the  volumes  for  each  diam- 
eter class  are  read  from  volume  tables. 

Allowance  for  defects  is  made  according  to  local  experience,  all  trees 
being  calipered  as   if  they  were  sound. 


"*  PARAGRAPH    LXI. 

THE     GRIDIRONING     METHOD. 

i.  Work  with  compass  (if  a  topographical  map  is  required,  also  with 
barometer  or  clinometer)  and  with  several  tapes  or  ropes.  These  ropes 
are  meant  to  denote  the  sides  of  a  strip;  within  the  strip  the  sectional 
areas  are  taken  with  calipers  or  Biltmore  sticks. 

2.  The  tapes  move  continuously  with  the  caliper  men,  and  there  is 
no  stopping.  The  compass  man  keeps  ahead  of  the  measuring  crew.  One 
of  the  outside  "tapers"  has  the  correct  length  desired  for  a  section.  His 
tape  must  be  run  straight.  The  inner  tapes  may  make  snake  linos.  The 
tally  man  uses  a  fresh  tally  sheet  for  each  section. 

3.  All  strips  lie  parallel  and  are  equidistant.  The  width  of  the  strips 
depends  on  the  density  of  growth,  smallest  diameter  calipered,  available 
help  and  accuracy  required. 

4.  The  distance  between  two  parallel  strips  depends  upon  accuracy  re- 
quired, width  of  strip  and  variety  of  configurations. 

5.  Each  strip  is  divided  into  sections  of  equal  length.  The  tally  sheet 
gives  for  each  section  the  diameters  (with  bark)  of  the  trees  in  that  sec- 
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traversed,  on  roads,  settlements,  existing  surveyor's  marks,  forest  fires, 
forest  pasture,  previous  lumbering  and  regeneration.  The  number  of 
seedlings  in  a  section  might  be  approximately  given  under  the  same  head. 


Forest  Mensuration 


39 


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40  Forest  Mensuration 

Advantages    of   the    gridironing    method    are : 

a.  A  topographical  map  is  obtained  at  a  slight  extra  expense.  The 
original  survey  is  controlled  and  the  area  of  the  tract  is  re-ascertained. 

b.  Cruisers  are  forced  to  traverse  all  sorts  of  country  and  are  not 
allowed    to    skip    swamps,   cliffs,    etc. 

c.  The  proportion  of  flats,  ridges,  slopes,  swamps,  farms,  or  farm 
soil,  pastures,  etc.,  is  found  at  the  same  time. 

d.  The  strips  may  be  used  as  permanent  statistical  sample  plots,  if 
they  start  from  definite  points  (corners)  and  run  in  definite  directions. 

e.  The  procession  of  the  cruisers  is  uninterrupted  by  stops;  hence  no 
loss  of  time. 

For  a  picture  of  a  convenient  tally  sheet  holder  see  Graves'  Handbook, 
page    123. 

The  gridironing  method  has  been  adopted  by  the  working  plan  division 
in  a  somewhat  altered  form  as  follows  (Bulletin  36,  page  120)  : 

1.  Strips  are  always  one  chain  (66  feet)  wide.  A  section  invariably 
comprises   one   acre   equaling   1  x  10  chains. 

2.  The  measuring  tape  is  trailing  in  the  center  of  a  strip ;  two  caliper 
men  (proceeding  one  at  the  left,  the  other  at  the  right  hand  of  the  tape) 
caliper  a  belt  one-half  chain  wide,  estimating  the  width  at  either  side 
of  the  central  tape. 

3.  The  compass  man  or  tally  man  with  the  front  end  of  the  tape 
attached  to  his  belt  goes  ahead  and  stops  at  the  end  of  every  chain, 
allowing  the  calipers   to  catch   up. 

4.  Thus  there  are  ten  stops  for  every  acre;  after  10  chains  the  tally 
man  enters  general  notes. 

5.  Heights  may  be  measured  by  a  separate  crew. 

A  crew  of  four  men  calipers  in  merchantable  timber  20  to  40  acres 
per  day;  in  small  and  merchantable  timber  from  15  to  25  acres  per  day; 
in  longleaf  pine   up  to  65   acres  per  day. 

PARAGRAPH    LXII. 

FOREST     RESERVE     METHODS. 

Roth's  Forest  Reserve  Manual  gives  three  methods  of  valuation  sur- 
vey, No.  1  and  No.  2  being  sample-area-methods,  and  No.  3  an  entire- 
area-method. 

I.  Sample  circles  with  a  radius  of  20  yards,  the  circle  containing 
J4  acre ;  the  radius  is  estimated,  or  paced  from  a  central  stick.  Two 
sub-methods    are   permitted,    namely : 

a.  Count  the  number  of  trees  of  merchantable  size ;  estimate  the  aver- 
age tree  according  to  log  length,  taper  and  thickness  of  bark;  estimate 
the  percentage  of  defectiveness  (from  10%  to  40%  after  Manual,  page  49). 


Forest  Mensuration  41 

b.  Caliper  the  trees  in  the  circle  into  two-inch  classes;  estimate  the 
average  tree  for  each  class  and  allow  for  defects  as  before. 

In  both  cases  a  map  must  show  the  site  of  the  sample  circles.  The 
circle  method  is  not  allowed  in  scattering  timber.  At  least  5%  of  the 
entire  area  must  be  sample-circled. 

2.  Sample  strips.  Strips  should  be  four  rods  wide,  should  run  across 
ridges,  should  be  shown  on  a  map.     Otherwise  proceed  as  under  1. 

3.  The  "forty"  method  is  used  on  surveyed  land.  It  is  an  entire-area 
method  applied  to  40  acres.  The  sides  of  a  "forty"  are  80  x  80  rods, 
equal   to   440  x  440  yards.     Prescriptions : 

ij.  Traverse  each  "forty"  on  lines  about  100  yards  apart,  thus  crossing 
4  times. 

b.  Halt  at  every  100  yards  and  estimate  the  trees  within  a  square  of 
100  yards   surrounding  the  stopping  place. 

c.  If  possible,  have  a  compass  man  control  the  length  and  the  direc- 
tion of  your  runs. 

PARAGRAPH    LXIII. 

SAMPLE    SQUARES. 

Sample  squares  containing  about  one  acre  are  used  in  Maine  and  in 
Northern  New  York.  The  side  of  a  sample  square  is  14  rods.  A  cruiser, 
from  the  center  of  the  square,  under  the  density  of  the  growth  existing 
in  Maine  and  New  York,  can  overlook  a  circle  of  7  poles  radius  sur- 
rounding him.  Hence,  as  a  matter  of  fact — or  rather  of  theory — he  skips 
the  corners  of  the  square,  counting  only  the  trees  in  a  circle  which  has 
the  side  of  the  square  for  its  diameter.  The  square  contains  196  square 
rods,  whereas  the  circle  of  7  poles  radius  contains  155  square  rods.  The 
cruiser  estimates  the  contents  of  all  trees  within  the  "square"  from  his 
central   standpoint. 

PARAGRAPH    LXIV. 

PISGAH      FOREST      METHOD     OF      1896. 

i.  The  diameters  of  all  trees  promising  to  yield  a  log  are  measured 
in  diameter  classes  of  ^2  foot  interval  by  a  crew  of  4  to  5  helpers  armed 
with   Biltmore  sticks. 

The  diameters  are  measured  (or  often  estimated  if  beyond  reach)  at 
the  point  above  which  the  tree  is  supposed  to  be  sound. 

2.  Each  tree  measured  is  marked  by  a  blaze.  The  foreman  enters  on 
a  tally  sheet  the  species  and  the  diameters  called  out  by  the  helpers.  A 
special  tally  sheet  is  used  for  each  cove. 

3.  The  average  contents  of  the  diameter  classes  are  estimated  with  the 
help  of  sample  trees  selected  for  each  species  and  each  diameter — a  very 
uncertain  estimate  owing  to  the   unsoundness  of  the  trees. 


42 


Forest  Mensuration 


4.     Each    cove    is   numbered   or   lettered   to   correspond    with    the   tally 
sheet  on  a  tree  standing  at  the  outlet  of  the  cove. 


PARAGRAPH    LXV. 

PISGAH    FOREST     METHOD    FOR    STUMPAGE    SALE,    BARK     SALE    AND    LUMBERING 

OPERATIONS. 

i.  Each  tree  is  approached  individually,  its  diameter  measured  and  its 
defects,  especially  its  hollowness,  examined  by  "sounding."  The  diam- 
eter measure  and  the  estimated  volume  are  entered  on  a  tally  sheet  oppo- 
site the  number  of  the  tree,  which  is  inserted  in  the  stump  of  the  tree 
by  a  stroke  of  the  "revolving  numbering  hammer." 

2.  One  cruiser  and  one  helper  tally  400  trees  per  day. 

3.  The  method  allows  of  ready  control  by  the  owner,  the  forester  and 
the  buyer.  It  is  adapted  to  hardwood  forests  in  a  rough  mountainous 
country  where  the  merchantable  trees  per  acre  are  few;  and  where  no 
tree  is,  practically,  free  from  defects.  (Compare  Graves'  Bulletin  No. 
36,  page   115). 

PARAGRAPH    LXVI. 

HENRY   GANNETT'S    METHOD,   ADOPTED  FOR  THE  TWELFTH   CENSUS. 

i.  Base  the  estimate  on  the  cruising  reports  obtainable  from  the  local 
lumber  companies  and  railroad  companies. 

2.  Control  the  applicability  of  the  estimates  to  huge  tracts  by  .travers- 
ing them  and  by  overlooking  them  from  a  mountain  top. 

Mr.  Gannett  expects  that  mistakes  made  in  one  county  will  be  offset 
by  those  made  in  another. 

PARAGRAPH    LXVII. 

A    "FORTY"    METHOD    USED    IN    MICHIGAN. 

1.  A  "forty"  (a  square  of  80  x  80  poles)  is  subdivided  into  10  rectan- 
gles  of  4  acres   each,   measuring   16  x  40   rods. 

2.  The  cruisers  estimates  when  entering  a  rectangle.  He  counts  the 
number  of  trees  on  every  4  acres  and  multiplies  the  number  by  the  size 
of  the  average  tree. 

3.  For  each  "forty"  the  cruiser  records  in  a  memorandum  the  factors 
influencing  the  logging  operations  or  the  timber  values,  notably  the 
swamps,  ridges,  forest  fires,  degree  of  defectiveness,  facilities  of  trans- 
portation. 

A  central  line  traversing  the  "forty"  in  a  north  and  south  direction  is 
sometimes  kept  by  a  compassman  assisting  the  cruiser.  The  outer  lines 
of  the  "forty"  are  plain  from  the  official  survey  marks. 


Forest  Mensuration  43 

A  number  of  variations  of  this  method  exist,  according  to  the  custom 
of  local  cruisers  and  according  to  the  predilections  of  the  lumbermen, 
largely  governed  by  the  value  of  stumpage.  Compare  Graves'  Bulletin  36, 
page    116. 


PARAGRAPH  LXVIII. 

DR.     FERNOW'S     "FORTY"     METHOD     USED    AT    AXTON. 

i.  Each  "forty"  is  subdivided  into  16  squares  of  2^2  acres  each,  the 
sides    of   a    square   being   20  x  20   poles. 

2.  The  head  estimator,  stepping  from  the  corner  of  the  square  10 
poles  east  (or  west)  and  10  poles  north  (or  south)  places  himself  in 
the  center  of  the  square. 

3.  Helpers  (students)  are  sent  out,  four  in  number,  towards  the  north- 
east, northwest,  southeast  and  southwest,  each  helper  reporting  the  diam- 
eter and  species  of  the  trees  found  in  that  one-quarter  of  the  2^  acres 
which  is  allotted  to  him. 

4.  The  "forties"  are  carefully  surveyed  and  surrounded  by  carefully 
trimmed  lines.     The  outlines  of  the  2^2  acre  sections  are  merely  paced. 


CHAPTER  II.— AGE 

PARAGRAPH    LXIX. 

AGE    OF    TREES    CUT    DOWN. 

The  age  of  trees  cut  down  is  found  by  counting  the  annual  rings  on 
a  cross  section  (preferably  an  oblique  cut)  made  as  low  above  the  ground 
as  possible.  Allowance  must  be  made  for  the  "stump  years,"  by  which 
is  understood  the  number  of  years  required  by  the  top  bud  of  the  seed- 
ling, after  sprouting,  to  reach  the  stump  height  ("cutting  height,"  after 
Circular  445). 

Ring-counting  in  the  case  of  even-porous  hardwoods  requires  the  use 
of  a  lens  and  of  some  coloring  liquid  (aniline  and  ferro-chloride)  on  a 
disc  planed  with  a  knife,  a  chisel  or  a  hollow  planer. 

The  difference  of  the  ring-numbers  on  the  stump  and  the  ring-num- 
bers at  any  place  higher  up  indicates  the  number  of  years  used  by  the 
top  bud  of  the  tree  to  traverse  the  intervening  distance.  Endogenous 
trees   do  not  form  any  rings. 

False  rings  are  formed  under  the  influence  of  late  frost,  early  frost, 
drought,  fire  and  insect  pests.     They  do  not  run  all  around  the  tree. 


44  Forest  Mensuration 

As  long  as  the  tree  lives,  it  must  annually  form  a  ring  of  growth  (or 
rather  an  additional  coat,  the  sleeves  of  which  cover  the  branches),  the 
outside  of  which  becomes  a  layer  of  bark,  the  inside  of  which  is  a  layer 
of  wood.  In  tropical  countries  this  rule  does  not  hold  good  provided 
that   there   is   no   change   of   season. 

The  formation  of  rings  in  the  branches  is  regular.  Branch-rings  are, 
however,  eccentric  and  elliptical.  The  formation  of  rings  in  the  roots 
is  said  to  be  irregular,  not  representing  the  age  of  the  root,  possibly  be- 
cause there  is  no  or  little  change  of  seasons  in  the  soil. 


PARAGRAPH    LXX. 

AGE    OF    STANDING    TREES. 

The  age  of  standing  trees  can  be  estimated  only  when  regular  annual 
whorls  of  branches  can  be  counted. 

The  records  of  seed  years  and  the  history  of  the  forest  kept  by  many 
forest  administrations  usually  give  an  idea  of  the  age  of  the  trees. 


PARAGRAPH  LXXI. 

AGE    OF    A    FOREST. 

The  age  of  a  forest  is  the  average  age  of  the  trees  composing  it. 

In  the  case  of  a  thicket  suppressed  for  a  long  time  by  the  superstructure 
of  a  leaf  canopy  overhead,  a  so-called  "economic  age"  is  frequently  sub- 
stituted for  the  actual  age.  In  the  case  of  Adirondack  spruce,  for  ex- 
ample, a  diameter  of  I  inch  in  the  center  of  the  trunk  had  better  be 
counted,  as,  say,  15  years,  although  it  may  contain  as  many  as  60  rings. 

The  mean  age  of  an  uneven-aged  wood  is  defined  as  follows : 

1.  That  number  of  years  which  an  even-aged  wood  would  require  on 
the  same  soil,  in  order  to  produce  the  same  volume  as  is  now  at  hand. 

2.  That  number  of  years  which  an  even-aged  wood  would  require  in 
order  to  produce  at  the  time  of  maturity  the  same  volume  which  the 
uneven-aged  wood  is  likely  to  produce. 

The  latter  definition  is  scientifically  more  correct.  Unless  it  is  adopted, ' 
an  uneven-aged  wood  may  get  over  20  years  older  in  20  years,  owing 
to  the  fact  that  the  trees  dying  in  the  meantime  are  mostly  minors  in  age. 


Forest  Mensuration 


45 


CHAPTER  III.— INCREMENT 

SECTION  I.— INCREMENT  OF  A  TREE. 
PARAGRAPH    LXXII. 

THE     KINDS     OF     INCREMENT. 

The  following  kinds  of  increment  must  be  distinguished : 

a.  Increment  of  height,  diameter,  sectional  area  and  volume. 

b.  Current  annual  increment,  current  periodic  increment  and  total  in- 
crement. 

c.  Average  annual  increment,  average  periodic  increment  and  average 
increment  at  the  age  of  maturity. 

d.  Increment  of  the  past  and  increment  of  the  future. 

e.  Absolute  increment  and  relative  increment. 

The  increment  of  stems  cut  down  is  found  by  counting  and  measuring 
the    annual    rings    on    several    cross    sections. 

The  term  "stem"  or  "tree  analysis"  designates  an  investigation  into  the 
past  height  growth,  diameter  growth  and  volume  growth  of  a  tree. 

Circular  445  of  the  Bureau  of  Forestry  defines  the  term  "increment," 
somewhat  narrowly,  as  follows :  "The  volume  of  wood  produced  by  the 
growth  in  height  and  diameter  of  a  tree  or  of  a  stand." 

For  definition  of  the  term  "tree  analysis,"  see  Circular  445  of  Bureau 
of  Forestry. 

This   circular   distinguishes   between : 

1.  Stump-analysis,    being    a    tree    analysis    which    includes    measure- 

ments of  the  diameter  growth  at  given  periods  on  the  stump 
only,  no  matter  what  other  measurements  it  may  comprise ; 

2.  Section-analysis,    being    a    tree   analysis    which   includes    measure- 

ments   of   the    diameter    growth    at    given    periods    upon    more 
than  one  section  of  a  tree ; 

3.  Partial    tree    (stump    or   section)    analysis,    wherein    the    measure- 

ment of  the  diameter  growth  at  given  periods  covers  a  portion 
only   of   the   total    diameter   growth. 


PARAGRAPH    LXXIII. 

HEIGHT    INCREMENT. 

The  height  increment,  from  the  silvicultural  standpoint,  is  of  interest 
to  the   forester  dealing  with   mixed   woods. 

The  difference  between  the  number  of  rings  found  on  two  separate  cross 
sections  through  the  bole  indicates  the  number  of  years   which  the  tree 


46 


Forest  Mensuration 


has  required  to  grow  through  the  distance  lying  between  these  two  sec- 
tions. By  counting  the  number  of  rings  at  several  cross  sections,  one  of 
which  is  made  as  close  to  the  ground  as  possible,  the  current  and  the 
average  height  growth  (increment)  may  be  obtained  by  arithmetical  or 
by  graphical   interpolation. 

A  dense  cover  favors  height  increment.  In  rare  instances,  however, 
the  stand  of  saplings  or  poles  is  so  close  that  the  height  increment  of 
the   individual   suffers   from  lack  of  food. 


PARAGRAPH    LXXIV. 


THE    CURRENT     HEIGHT     INCREMENT. 


In  the  high  forest  the  current  annual  height  increment  reaches  a 
maximum  at  an  early  age;  passing  this  maximum,  it  sinks  more  or  less 
rapidly.  The  culmination  of  the  current  annual  height  increment  occurs 
the  much  earlier  and  its  slackening  after  said  culmination  goes  on  at  a 
more  rapid  rate  if 

i.     the  species  is   fast  growing  and  light  demanding; 

2.  the  tree  observed  belongs  to  the  dominant  class ; 

3.  the  soil  is  good. 

For  yellow  pine  the  culmination  of  the  current  annual  height  incre- 
ment occurs  amongst  dominant  saplings  between  the  10th  and  15th  years; 
for  spruce  at  about  the  20th  year ;  for  beech  and  fir  between  the  25th 
and  30th  years.  Suppressed  trees  show  the  maximum  of  current  height 
growth  much  later  than  dominant  trees. 

As  a  general  rule  for  all  species,  in  case  of  dominant  trees,  the  longest 
shoot  is  made  10  to  15  feet  above  ground.  Slow  growing  species,  shade 
bearers  and  trees  stocking  on  poor  soil  reach  that  level  at  a  later  date 
than  trees  and  species  growing  under  reversed  conditions. 

In  the  case  of  coppice  forest,  the  maximum  of  the  current  height 
growth  lies  in  the  first  three  years  of  the  life  of  the  shoot.  For  oak 
coppice,  the  following  table  may  serve  as  an  illustration  of  height  growth : 

Growth  in  Feet. 


Age  in  years 

10 

20 

30 

40 

5o 

Actual  height 

13' 

23' 

30' 

37' 

43' 

Current  annual  increment 

1.3' 

1.0' 

0.7' 

0.65' 

0.63' 

PARAGRAPH    LXXV. 

THE     AVERAGE     HEIGHT     INCREMENT. 


The  average  annual  height  increment  culminates  later  than  the  current 
annual  height  increment,  and,  after  the  culmination,  it  decreases  at  a  less 


Forest  JMcnsuration  47 

rapid  rate  than  the  current  annual  height  increment.  The  average  annual 
height  increment  culminates  at  the  very  age  at  which  it  is  equal  to  the 
current  annual  height  increment. 

As  long  as  the  average  increment  increases  the  current  increment  is 
larger  than  the  average.  The  average  increment  still  rises  during  a  period 
of   decrease   of  current   increment. 

These  laws  hold  good  not  only  for  height  growth,  but  also  for  the 
growth  of  diameter,  sectional  area  and  volume.  They  are  based  merely 
on  mathematical  principles  and  are,  for  that  reason,  independent  of  spe- 
cies,  climate  and  soil. 

If  "a"  denotes  the  current  annual  increment,  and  if  "d"  denotes  the 
average  annual  increment,  whilst  the  indices  i,  2,  3,  etc.  (up  to  n),  indi- 
cate the  year  of  increment,  then  the  following  five  equations  hold  good : 

n  X  dn  =  aj  -(-  a2  -f  a3   +  an 

(n  4.  1)  dn  +  1  =  at   f  a,  +  a3 au  +  an  +1 

(n  +  1)  dn  +  1  =  n  X  dn  +  an  +  1 

n  X  dn  +  1  =  n  X  du  +  an  +  1  —  dn  +  1 
n  (dn  +  1  —  dn  )  =  an  +  1  —  dn  +  1 


PARAGRAPH    LXXVI. 

RELATIVE   INCREMENT   OF   THE    HEIGHT. 

The  percentage  of  height  increment  forms,  from  the  start  on,  an  irreg- 
ularly descending  progression. 

If  the  height  is  h  at  the  beginning  of  a  period  of  n  years  of  observa- 
tion and  H  at  the  end  of  that  period,  then 

h  X  1.  opn  equals  H 

and 
n 

p  equals  100.J—  —  100 

Pressler  substitutes  for  this  formula  in  case  of  short  periods  of  observa- 
tion   the   following : 

200         H  —  h 

n  H  +h 

This  formula  is  derived  as  follows :  Imagine  that  we  are  in  the  midst 
of   the    period    of    n   years.     At    that    time,    the    increment    is    apt    to    be 

— ^— ,  whilst  the  height  at  that  time  is  apt  to  be — :  hence,  for  that  mid- 

n  2 

die  year,  the  equation  is : 

p  H  —  h  2 

X 


100  n  H  +h 


48  Forest  Mensuration 

PARAGRAPH  LXXVII. 

DIAMETER    INCREMENT. 

The  current  diameter  increment  is  obtained  by  counting  and  measuring 
the  rings  on  a  disk  through  the  tree.  It  is  generally  best  to  count  from 
the  bark  towards  the  center,  along  two  radii  standing  perpendicular  to 
each   other. 

The  general  laws  of  diameter  growth  are  identical  with  those  of  height 
growth  relative  to  culmination,  decrease  and  increase  of  absolute  (Par- 
agraph LXXV.)  as  well  as  of  relative  (Paragraph  LXXVI.)  increment. 

If  we  exclude  the  butt-piece  below  chest-height,  the  annual  rings  along 
the  tree  bole  measured  at  various  elevations  above  ground  show  a  grad- 
ual increase  of  width  with  elevation,  provided  that  the  leaf  canopy  of 
the  forest  is  complete  and  uninterrupted — e.  g.,  the  width  of  the  ring  50 
feet  from  the  ground,  formed  in  1903,  is  greater  than  the  width  of  the 
ring  formed  20  feet  above  ground  in  the  same  year. 

For  trees  standing  in  open  crown-density,  the  width  of  the  ring  de- 
creases with  the  elevation  above  the  ground,  especially  within  the  crown 
itself. 

A  tree  standing  in  a  thin  crown-density  may  show  an  even  width  of 
ring  all  over  the  tree  bole. 

For  very  old  trees  in  closed  stand  it  is  sometimes  found  that  the  diam- 
eter, say  40  feet  above  ground,  is  larger  than  the  diameter,  say,  20  feet 
above  ground. 

The  rings  on  a  disk  are  not  actually  circles ;  they  more  closely  ap- 
proach the  form  of  eccentric  ellipses   (see  Paragraph  XIII.). 

» 

PARAGRAPH     LXXVIII.  * 

SECTIONAL    AREA     INCREMENT. 

The  increment  of  the  sectional  area  is  obtained  from  the  increment  of 
the  diameters.  Where  greater  exactness  is  required,  and  especially  in 
case  of  irregular  rings,  the  planimeter  or  the  weight  of  a  piece  of  paper 
having  the  form  of  the  sectional  area  may  be  used  for  measuring  to  good 
advantage    (Paragraph   XIII.). 

The  increment  of  the  sectional  area  at  chest  height  depends  on  the 
crown  density  overhead;  further,  on  the  quality  of  the  soil.  At  chest 
height  the  culmination  of  the  current  annual  sectional  area  increment 
takes  place,  in  the  case  of  dominant  trees,  fast  growing  species  and  com- 
plete  cover   overhead,   between   the   years   40  and   70. 

The  culmination  of  the  current  annual  sectional  area  increment  occurs 
always  later  than  the  culmination  of  the  current  height  and  diameter  in- 
crement.    After  culmination  it  remains  uniform  for  a  long  time. 

The  absolute  increment  of  a  sectional  area  higher  up  on  the  bole,  com- 
pared with  the  absolute  increment  at  chest  height,  is  found  to  be  equal 
to  it  in  the  case  of  dominant  trees ;  larger  in  the  case  of  suppressed  trees ; 
and  smaller  in  the  case  of  isolated  trees. 


Forest  Mensuration  49 

Pressler  establishes  as  the  "law  of  bole  formation"  the  following  rule : 
"The  absolute  increment  of  the  sectional  area  at  any  point  of  a  bole  is 
directly  proportioned  to  the  leaf  surface  above  that  point." 

This  rule  is,  on  the  whole,  correct.  An  unexpected  swelling,  however, 
is  often  found  at  9/16  of  the  height  of  the  tree.  Within  the  crown  of 
the  tree,  the  decrease  of  sectional  area  increment  is  rapid. 


PARAGRAPH    LXXIX. 

RELATIVE    INCREMENT    OF    DIAMETER    AND    OF    SECTIONAL    AREA. 

The  increment  percentage  at  any  point  of  the  bole,  like  all  increment 
percentages,  forms  a  constantly  but  irregularly  descending  progression. 

At  any  point  of  the  bole  the  increment  percentage  of  the  sectional  area 
is  the  double  of  the  increment  percentage  of  the  diameter. 

Schneider  gives  a  handy  formula  for  the  sectional  area  increment  per- 
centage, viz. : 

400 

P  equals   

H  nd 

wherein  d  represents  the  diameter  at  the  beginning  of  the  period  of  ob- 
servation, and  wherein  n  indicates  the  number  of  rings  per  inch  at  the 
time  of  observation. 

The  percentage  of  the  sectional  area  increment  increase  along  the  bole 
with  increasing  height  of  the  disk  measured,  excepting,  however,  possibly, 
the  case  of  very  isolated  trees. 

The  average  sectional  area  increment  percentage  of  the  bole  is  found  at 
a  point  a  little  below  one-half  of  the  total  height,  namely,  at  about  0.45 
of  the  total  height  from  ground. 


PARAGRAPH  LXXX. 

VOLUME     INCREMENT. 

The  (current  and  future)  volume  increment  of  standing  trees  is  of 
great  interest  to  forest  financiers ;  it  can  be  estimated  only,  and  cannot 
be   measured    exactly. 

The  volume  increment  of  trees  cut  down  may  be  ascertained  as  follows : 

1.  By  the  sectional  method,  or  by  "section  analysis"  (Paragraph 
LXXXL). 

2.  From  the  increment  of  sectional  area  chest  high,  height  increment 
and  form  figures   (Paragraph  LXXXIV.). 

3.  From  the  increment  of  sectional  area  in  the  midst  of  bole  (Para- 
graph LXXXV.). 

4.  On  the  basis  of  the  average  annual  increment  (Paragraph 
LXXXVIL,   last  4  lines). 

5 


V 


50 


Forest  Mensuration 


PARAGRAPH  LXXXI. 


SECTION    ANALYSIS. 


The\section-method  is  a  complete  tree  analysis  by  sections.  The  entire 
bole  is  divided  into  a  number  of  sections,  preferably  of  even  length,  at 
both  ends,  or,  better,  in  the  midst  of  which  the  periodical  increment  of 
the  sectional  area  is  ascertained   (compare  Paragraph  XL). 

In  the  latter  case,  multiplying  such  sectional  areas  (in  square  feet) 
as  belong  to  the  same  age  of  the  tree  by  the  length  (in  feet)  of  the  sec- 
tions, the  volumes  (in  cubic  feet)  of  the  different  sections  at  given  ages 
are  obtained. 

The  "top  pieces,"  however,  must  be  figured  out  separately,  their  length 
differing  from  the  even  length  of  the  sections.  These  top  pieces  are 
usually  considered  as  cones,  and  their  volumes  are  ascertained  as  one-third 
height  times  basal  area  of  top  piece.  The  basal  area  of  the  top  piece  is 
identical  with  the  upper  area  of  the  uppermost  full  section  of  a  given  age. 


Example  for  Huber-Sections  Ten  Feet  Long. 


Total  height 

25  feet. 

40  feet. 

67  feet. 

Total  age 

20  years. 

40  years. 

60  years. 

Sectional  area  of  Section  i 

0.34  sq.  ft. 

0.78  sq.  ft. 

1.23  sq.  ft. 

Sectional  area  of  Section  2 

0.15  sq.  ft. 

0.45  sq.  ft. 

0.87  sq.  ft. 

Sectional  area  of  Section  3 

0.25  sq.  ft. 

0.  64  sq.  ft. 

Sectional  area  of  Section  4 

0.03  sq.  ft. 

0.53  sq.  ft. 

Sectional  area  of  Section  5 

0.25  sq.  ft. 

Sectional  area  of  Section  6 

0.04  sq.  ft. 

Summary  of  sectional  areas 

0.49  sq.  ft. 

1.5 1  sq.  ft. 

3.56  sq.  ft. 

Summary  sectional  areas  x  10 

4.90  cu.  ft. 

15.10  cu.  ft. 

35.60  cu.  ft. 

Volume  of  top  piece 

0.05  cu.  ft. 

0.09  cu.  ft. 

0  08  cu  ft 

Total  volume 

4.95  cu.  ft. 

15.19  cu.  ft. 

35.68  cu.  ft. 

The  volume  of  the  top  pieces  forms  in  the  older  age  columns  an  insig- 
nificant part  of  the  total  volume. 

If  the  logs  as  cut  in  the  woods  are  used  as  sections,  then  each  section 
has  a  separate  length  and  its  volume  must  be  separately  ascertained  for 
every  decade  of  age  of  tree. 

Remark  :  It  is  wise  to  first  ascertain  the  full  age  of  the  tree,  allowing 
for  stump  years.  It  is  further  wise  to  throw  off  that  number  of  years 
which  exceeds  full  decades — e.  g.,  in  case  of  a  tree  117  years  old,  7  years. 


Forest  Mensuration  51 

At  the  stump  the  rings  had  best  be  counted  from  the  inside  out,  allowing 
for  stump  years.  Instance:  Age  of  tree,  117;  stump  years,  4  years;  count- 
ing on  the  stump,  from  the  inside,  6  rings  establishes  the  ring  formed  in 
the  year  10.  Continuing,  the  rings  of  the  years  20,  30,  40,  50,  etc.,  up 
to  year  no,  are  pencil  marked.     The  outside  seven  rings  are  thrown  off. 

At  all  other  disk-sections,  count  and  measure  from  the  outside  in,  after 
discarding  the  7  years  exceeding  full  decades  of  tree  life. 

PARAGRAPH    LXXXII. 

noerdlinger's    paper   weight    method. 

The  total  length  of  the  tree  is  divided  into  8  Huber  sections,  and  cuts 
are  made  in  the  midst  of  these  sections,  at  the  height  of  1/16,  3/16,  5/16, 
7/16  and  up  to  15/16  of  the  bole.  On  each  cross  section  the  radii  are 
measured,  not  with  the  rule,  but  with  dividers. 

On  a  piece  of  paper  folded  4  times  and  thus  divided  into  8  sectors  the 
measurements  are  entered  with  the  help  of  the  dividers,  one  sector  being 
allotted  to  the  first  cross  section,  the  next  sector  to  the  next  cross  sec- 
tion, etc.  Multiplying  the  total  weight  of  the  zone  indicating,  say,  the 
year  70,  by  height  of  the  tree  and  dividing  the  product  by  the  weight  of 
a  square  foot  of  paper,  the  volume  of  the  tree  when  70  years  old  is 
directly  obtained  in  cubic  feet.  Similarly  the  zones  corresponding  with 
the  year  50,  60,  etc.,  are  cut  out,  weighed  and  multiplied. 

If  the  volume  increment  percentage  p  alone  is  to  be  obtained,  then  it 
is  enough  to  divide,  say,  the  "weight"  of  the  year  70  by  the  weight  of 
the  year  60,  and  the  10th  root  of  the  quotient  will  equal  i.op. 

PARAGRAPH   LXXXIII. 
schenck's  graphic  tree  analysis. 
Graphic  tree  analysis  offers  the  following  advantages : 

1.  Mistakes  are  impossible,  being  at  once  noticeable  on  the  diagram 
paper. 

2.  The  volume  in  feet  Doyle  can  be  readily  obtained  for  any  stated 
minimum    diameter. 

3.  The  graphical  sketch  is  adaptable  to  any  of  the  43  scales  in  use  in 
the  United  States,  as  well  as  to  the  metric  system. 

4.  The  thickness  of  heart  wood  and  sap  wood  and  bark  readily  appears. 

5.  It  is  immaterial  whether  measurements  are  taken  in  meters  or  in 
feet,  the  graphical  sketch  readily  allowing  of  transfers  into  other  units. 

6.  Height  growth  and  diameter  growth  appear  at  the  same  time,  and 
from  the  same  entries. 

7.  The  length  of  the  sections  taken  need  not  be  uniform. 

The  method  of  proceeding  is  as  follows :  On  millimeter  paper  a  system 
of  co-ordinates  is  established;  heights  are  entered  as  ordinates,  diameters 


52 


Forest  Mensuration 


or  radii  as  abscissas.  The  scale  for  the  height  entries  should  be  much 
smaller  than  that  of  the  diameter  entries. 

Diameter  points,  at  the  different  section-heights,  corresponding  to  a 
given  decade  of  years  are  joined  (beginning  at  the  outside),  by  which 
procedure  the  outline  of  the  tree  at  that  decade  is  established. 

Th  top  cones  are  obtained  by  prolonging  such  outlines  arbitrarily  until 
they  intersect  with  the  height-axis. 

The  merchantable  bole  for  each  decade  is  dissected,  on  the  diagram, 
into  logs  the  length  and  diameter  of  which  are  measured  on  the  diagram. 


PARAGRAPH   LXXXIV. 

wagener's  method  and  stump  analysis. 

Wagener  recommends  a  partial  stem  analysis  for  cases  in  which  a 
knowledge  of  the  absolute  increment,  not  a  knowledge  of  the  absolute 
tree  volume,  is  required.  Tree  volume  is  sectional  area  chest  high  times 
height  of  tree  times   form  factor. 

Wagener  analyses : 

a.  the  height  growth  by  counting  the  rings  at  various  altitudes  along 
the   bole ; 

b.  the  growth  of  the  sectional  area  at  chest  height  by  measurement  in 
decades  in  the  usual  way. 

Wagener  then  estimates  the  form  factor  according  to  form  factor  tables. 

In  the  latter  proposition,  obviously,  lies  the  danger  of  mistakes.  Since, 
however,  increment  is  a  difference  of  volumes,  merely  the  difference  of 
mistakes — a  comparatively  small  item — enters  into  the  problem.  ► 


Age  in  years 

60 

80 

100 

120 

14- 

17- 

19- 

21 . 

Sectional  area  b.  h 

0.  25 

0.35 

0.50 

0.71 

Height  in  feet 

75- 

85- 

93- 

105. 

Form  factor 

0.50 

0.50 

0.50 

050 

Volume  in  cubic  feet 

9-4 

13- 

23- 

36. 

3- 

5              ic 

).              1 

3- 

The  "stump  analysis"  (compare  Paragraph  LXXII.)  introduced  by 
the  Bureau  of  Forestry  rests  on  premises  similar  to  those  proffered  by 
Wagener. 

If  the  form  height  for  the  stump-diameters  (or  the  number  of  feet 
b.  m.  per  square  foot  of  stump  area  for  given  stump  diameters)  is  known, 
the  rate  of  volume  increment  can  be  quickly  ascertained  by  mere  stump 
analysis. 


Forest  Mensuration  53 

It  is,  however,  a  well  known  fact  that  the  diameter  growth  at  the 
stump — especially  at  a  low  stump — is  particularly  unreliable  as  an  index 
of  volume  growth,  owing  to  the  exaggerating  influence  on  stump  growth 
exercised  by  light,  by  water,  by  depth  of  soil  and  by  superficial  roots. 

Stump  analysis  as  a  means  to  bring  a  volume  in  reference  to  a  sec- 
tional area  at  the  stump  is  permissible  only  as  a  necessary  evil. 

PARAGRAPH    LXXXV. 

pressler's   method. 

Frequently  the  task  before  the  forester  is  merely  that  of  ascertaining 
the  increase  of  bole  volume  during  the  last  10  or  20  years.  Then  after 
Pressler,  one  single  investigation  into  the  growth  of  the  sectional  area  is 
sufficient  when  made  with  the  help  of  the  accretion  borer  in  the  midst  of 
the  "decapitated"  bole.  The  volume  increment  in  cubic  feet  equals  the 
sectional  area  increment  in  question  multiplied  by  the  height  of  the 
tree. 

The  bole  is  decapitated  by  that  number  of  top  shoots  which  have  been 
formed  during  the  period  of  observation.  This  operation  corresponds 
very  well  with  the  usual  practice  of  judging  the  bole  increment  per- 
centage from  the  sectional  area  increment  ascertained  at  0.45  of  height 
of  tree. 

Pressler  measures  the  sectional  area  at  the  end  of  the  period  of  observa- 
tion too  large,  measuring  it  at  too  low  a  point.  He  multiplies  this  sec- 
tional area,  however,  by  too  small  a  height — namely,  the  decapitated 
height;  thus  a  mistake  made  in  the  positive  sense  is  apt  to  be  eliminated 
by  a  mistake  made  in  the  negative  sense. 

The  axe  can  be  used  to  better  advantage  frequently  than  the  accretion 
borer. 

PARAGRAPH   LXXXVI. 
breymann's  method. 
Breymann  gives  the  following  formula :  '  Kic^ 

1.     For  the  current  annual  volume  increment  T:  ^  "^.^, 


T  =  V(3d+T)        <~*^^^^~i   ) 


wherein  "8"  and  "A,"  denote   the   annual   increase   of   diameter  "d"  and 
length  ''1"  respectively. 

2.     For  the  corresponding  increment  percentage  P: 

8       X 


P  =  100(2-+T) 


It  appears  that  for  trees  of  old  age  and  hence  of  little  height  growth 
the  increment  percentage  is  merely  dependent  on  the  diameter  increase. 


54 


Forest  Mensuration 


Breymann,   however,   neglects : 

1.  The  change  of  form  figure,  during  the  period  of  observation; 

2.  A  number  of  small  factors  which  ought  to  be  embraced  in  the 
formula. 

For  stopping  height  growth  or  for  A,  =  0  ,  the  term  given  for  P  can 
be  easily  reduced  to  the  term  given  by  Schneider  for  the  sectional  area 
increment   percentage. 


' 


■  ~ -^  PARAGRAPH    LXXXVII. 

FACTORS    INFLUENCING    THE    CUBIC   VOLUME    INCREMENT. 


*M* 


■ 


A. 


The  culmination  of  the  current  annual  volume  increment  takes  place  at 
a  later  year  than  the  culmination  of  the  sectional  area  increment  at  breast 
■  •  height.  Naturally  so,  because  with  increasing  age  of  a  tree,  its  root  sys- 
tem as  well  as  the  branch  system,  the  feeders  of  the  body,  show  contin- 
uous increase. 

Big  and  long  branches,  of  course,  require  a  great  deal  of  wood  fibre 
to  increase  and  maintain  their  own  strength,  like  levers  increased  in 
length.  Hence,  from  a  certain  size  of  branch  on,  all  wood  fibre  produced 
by  the  branch  is  used  up  within  the  branch  itself,  for  its  own  purposes, 
instead  of  being  added  as  increment  to  the  merchantable  bole. 

After  Dr.  Metzger,  the  crown  of  a  tree  yields  the  maximum  of  bole 
increment  if  its  crown  diameter  is,  and  if  the  number  of  trees  per  acr<* 
are: 


Quality  of  soil. 

Diameter  of  crown,  in  feet. 

No.  of  trees  per  acre. 

Very  good. 

16.5 

203 

Good 

14-7 

256 

Medium 

12.7 

343 

Poor 

9-3 

640 

Very  poor 

8.3 

807 

From  the  theoretical  standpoint  it  seems  wise,  consequently,  to  force 
the  lower  branches  of  a  tree  to  die,  with  the  help  of  proper  tension  and 
friction  within  the  leaf  canopy,  when  they  exceed  a  length  of  8.25,  7.35, 
6.35,  4.65  and  4.15  feet  respectively  (the  halves  of  the  diameters). 

Metzger's  investigations  are  interesting,  but  his  conclusions  seem  to  be 
too  sweeping. 

P.  P.  Pelton  recommends  the  lopping  of  branches  in  order  to  shorten 
the  length  of  the  branch-levers. 

The   average   annual   volume   increment   of   dominant   and    sound   trees 


Forest  Mensuration 


55 


culminates  at  a  very  high  age  only,  if  ever,  owing  to  the  late  culmina- 
tion of  the  current  annual  average  increment. 

The  volume  increment  percentage  forms — as  in  all  cases  of  increment — 
a  steadily  but  irregularly  decreasing  progression.  This  percentage  is  in- 
variably equal  to  or  higher  than  the  sectional  area  increment  percentage 
at  chest  height. 

Roughly  speaking,  the  volume  increment  percentage  amounts  to  from 
i  to  1.7s  times  the  sectional  area  (at  chest  height)  increment  percentage, 
or,  as  Pressler  gives  it,  to  from  2  to  3^2  times  the  diameter  (at  chest 
height)   increment  percentage. 


Crown;'covers  part  of  bole 


■>. 


£  or  more. 

itot 

Less  than  \. 


Wo 


>X  *  Height  Growth. 


Seemingly  nil. 


2.67 


Medium. 


2 .  67  -  <  •> 


Good 


v    G°* 


.3.00  .« 
1-33UC 


Excellent. 


W  t>ti  ■■>   ■>  ■-  <  *  -  > 


3-i7U*^ 
3-33-1,1*  V* 


#\ 


■V- 


Since  the  average  volume  increment  of  a  tree  is  equal  or  closely  equal 
to  the  current  annual  increment  at  a  high  age  only,  it  is  usually  not 
permissible  to  substitute  the  average  increment,  which  is  easily  ascer- 
tained, for  the  current  annual  increment. 


PARAGRAPH    LXXXVIII. 

VOLUME-INCREMENT    PERCENTAGE   OF    STANDING    TREES. 

In  the  case  of  standing  trees  the  volume  increment  percentage  cannot 
be  measured,  owing  to  the  impossibility  of  ascertaining  a  change  of  form 
height. 

The  Pressler  data  given  in  the  preceding  paragraph  allow  of  estimating 
the  volume  increment  percentage  of  standing  trees  on  the  basis  of  a 
diameter-increase,  measured  at  breast  height. 

The  Pressler  "accretion  borer"  is  used  for  the  purpose,  or  an  axe. 

Stoetzer,  Director  of  the  Forest  Academy  at  Eisenach,  modifies  the 
Schneider  formula  for  sectional  area  percentage,  writing  it 

C 
P  =  n¥ 

wherein  n  indicates  number  of  years  (rings)  required  to  form  one  inch; 
d  represents  the  diameter  at  the  beginning  of  the  period  of  investigation, 
whilst  C  (the  so-called  "constant  factor  of  increment,"  which  is  not  a 
constant  factor  at  all)  must  be  ascertained  for  a  given  species,  soil,  diam- 
eter, age  and  position  by  actual  tests  on  felled  trees. 

In  old  dense  beech  woods  C  is,  e.  g.,  540.  After  a  seed  cutting  in  the 
same  woods  during  the  final  stage  of  regeneration  C  is  only  450  (observa- 
tion by  Dr.  Wimmenauer). 


56  Forest  Mensuration 

Trees  growing  as  cones  would  grow,  have  C  equal  to  600;  trees  grow- 
ing as  Apollonian  paraboloids  would  grow,  have  C  equal  to  800;  after 
Stoetzer,  C  might  amount  to  as  much  as  930,  in  case  of  suppressed  trees. 
The  minimum  possible  (in  sound  trees)   for  C  is  400. 

The  Pressler  values  given  in  the  table  of  the  preceding  paragraph 
closely  correspond  with  the  constant  factors  of  increment  ascertained 
after  Stoetzer.  In  the  case  of  the  Pressler  table  (at  end  of  Paragraph 
LXXXVII.)  we  find,  for  medium  height  growth  and  very  small  crown, 
a  factor  3.00  by  which  the  diameter  increment  percentage  is  to  be  multi- 
plied. This  factor  3.00  corresponds  with  600  for  a  constant  factor  of  in- 
crement. 

If  the  diameter  in  the  midst  of  the  bole  is  l/2  of  the  diameter  at  the 
end,  then  the  tree,  it  seems,  is  conical,  and  an  increment  factor  of  600 
might  be  assumed.  If  the  sectional  area  in  the  midst  of  the  bole  equals 
y2  the  sectional  area  at  the  end,  then  the  tree  is  a  paraboloid,  and  the 
increment  factor  seems  apt  to  be  800. 

It  must  be  remembered,  however,  that  a  tree  forming  a  paraboloid 
grows  as  a  paraboloid  only,  if  its  percentage  of  height  growth  is  equal  to 
its  percentage  of  growth  of  sectional  area — a  rare  case  in  merchantable 
trees. 

Similarly,  a  tree  growing  as  a  cone  must  have  the  height  increment 
percentage  equal   to   its   diameter  increment  percentage. 

If  n  and  v  represent  the  number  of  rings  per  inch  added  to  original 
diameters  d  and  8  at  chest  height  and  at  0.45  of  the  height  of  the  tree 
respectively,  then  the  "constant  factor  of  increment  C"  is  found  as  follows : 

400         C 

p  (volume) 


v8       nd 
nd 


C  =  400- 


PARAGRAPH    LXXXIX. 

INTERDEPENDENCE    BETWEEN    CUBIC    INCREMENT    AND    INCREMENT 
IN     FEET    B.     M.     DOYLE. 

Doyle's  rule  under-estimates  the  contents  of  small  logs  and  over-esti- 
mates  those   of  big  logs. 

Consequently,  the  growth  of  a  tree  bole  in  feet  b.  m.  Doyle  is  (for 
small  trees  yielding  logs  under  28"  diameter)  relatively  faster  than  the 
growth  of  a  tree  bole  expressed  in  cubic  feet.  The  figures  of  Column  D 
denote,  in  the  following  table,  this  excess  rate  of  growth : 


Forest  Mensuration 


57 


A 

5 

C 

D 

No.  of  ft.  b.  m.  per 

Differences  of  con- 

"Extraordinary" 

Diameter  of  logs 

one  eu.  ft.  of  tim- 

secutive   figures   in 

percentage  of  incre- 

without bark. 

ber  estimated 

Column  B. 

ment  Doyle  co-in- 

after  Doyle. 

ciding  with 
1"  growth. 

12" 

509 

0.41 

S.i 

13" 

5  SO 

o.35 

6.4 

14" 

5-35 

0-33 

5-7 

15" 

6.18 

0.26 

4.2 

16" 

6.44 

0.27 

4-3 

17" 

6.71 

0.22 

3-3 

18" 

6-93 

0. 14 

2. 1 

19" 

7.07 

0.26 

3-2 

20" 

7-33 

0.18 

2-5 

21" 

7-51 

0. 16 

2.2 

22" 

7.67 

0.15 

2.0 

23" 

7.82 

0.13 

i-7 

24" 

7-95 

0. 14 

1.8 

25" 

8.09 

0. 11 

i-4 

26" 

S.20 

0.12 

1-5 

27" 

8-33 

0.09 

1 . 1 

28" 

8.41 

0. 11 

1 . 1 

29" 

8.52 

0.08 

1 .0 

30" 

8.60 

... 

For  the  standard  rules,  the  increment  percentage  of  a  tree  can  be  ascer- 
tained by  cubic  measure  as  well  as  by  standard  measure. 

If  n  years  are  required  to  form  one  additional  inch  of  diameter,  then 
the   extraordinary   percentage   of   Doyle-increments    amounts    annually   to 


yl.OD,  wherein  D  represents  the  values  of  Column  D  in  the  foregoing 
table. 


By  this  factor  -j/l.OD,  the  cubic  volume  increment  percentage  of  a 
bole  may  be  converted,  ceteris  paribus,  into  Doyle  increment  percentage, 
provided  that 


58  Forest  Mensuration 

i.  The  cubic  increment  percentage  of  the  total  bole  coincides  with  the 
cubic  increment  percentage  of  the  merchantable  bole ; 

2.  The  merchantable  bole  does  not  increase  in  length  during  the  period 
of    observation. 

PARAGRAPH    XC. 

CONSTRUCTION     OF     VOLUME     TABLES. 

Volume  tables  are  "tree  yield  tables"  from  which  the  volume  of  a  tree 
of  given  species,  given  age,  given  diameter  breast  high  or  stump  high, 
given  height,  given  merchantable  bole,  given  position  (suppressed,  dom- 
inant, etc.,  or  isolated,  crowded,  etc.),  given  locality  and  so  on  can  be 
readily  read.  The  units  of  volume  are  cubic  feet,  board  feet,  standards, 
cords,  etc.,  according  to  the  requirements  of  the  case. 

Obviously,  volume  tables  give,  or  should  give,  the  volumes  of  average 
trees ;  they  may  give,  in  addition,  the  maximum  and  minimum  volume 
possible  in  a  tree  of  stated  description. 

Volume  tables  are  constructed  either  on  the  basis  of  hundreds  (thou- 
sands) of  measurements  taken  from  trees  actually  felled  in  the  woods 
(possibly  also  sawn  at  a  saw  mill,  to  ascertain  the  grades)  or  on  the 
basis  of  a  smaller  number  of  complete  section  analyses. 

The  rapidity  of  volume  growth  of  a  species  and  the  development  of  its 
form  height  depend  on  many  local  factors — notably  on  climate,  soil,  sylvi- 
cultural  systems  at  hand,  influence  of  fires,  fungi,  insects,  etc. 

Owing  to  the  multitude  of  local  factors  influencing  the  volumes  and 
the  changes  of  volumes,  local  volume  tables  alone  are  entitled  to  &  place 
in  exact  mensuration. 

Volume  tables  for  second  growth  are  more  reliable  than  volume  tables 
for   first   growth. 

Circular  445  of  Bureau  of  Forestry  defines  volume  table  as  "a  tabular 
statement  of  the  volume  of  trees  in  board  feet  or  other  units  upon  the 
basis  of  their  diameter  breast  high,  their  diameter  breast  high  and  height, 
their  age,  or  their  age  and  height." 

The  method  of  construction  of  volume  tables  is  either  mathematical  or 
graphical. 

1.    Mathematical  method. 

The  volumes  ascertained  for  trees  of  a  given  diameter  (breast  high  or 
stump  high  with  or  without  bark),  a  given  merchantable  length  or  total 
length,  a  given  age  or  a  given  quality  or  locality  are  added  up. 

The  sum  total  of  these  volumes  divided  by  the  number  of  trees  forming 
it  yields  the  average  volume  of  the  tree  of  stated  description. 

These  averages  are  shown,  for  the  various  diameters,  lengths,  ages  and 
localities,  in  tabular  form. 

The  volumes  corresponding  with  such  diameters,  lengths,  ages  and  lo- 
calities, for  which  sample  trees  were  not  cut  and  measured,  are  found  by 
arithmetic  interpolation. 


Forest  Mensuration  59 

Finally,  the  differences  in  volume  shown  by  average  trees  of  similar 
description  (1.  e.,  differing  but  slightly  in  diameter,  length,  etc.)  are 
formed  and  rounded  off  in  a  manner  causing  the  volumes  to  show  a  more 
steady  mathematic   progression. 

2.     Graphic  method. 

The  volume  of  each  tree  measured  is  entered  as  the  abscissa  on  a 
diagram-system  of  co-ordinates,  whilst  the  diameters  of  the  trees  (or  the 
age,  etc.)  are  registered  on  the  ordinate  axis.  Similarity  of  length  is  in- 
dicated by  color  of  mark  representing  the  tree;  similarity  of  locality  is 
indicated  by  the  form  of  the  mark  (square,  triangle,  cross,  circle,  etc.). 

Corresponding  marks  are  then  joined  by  chains  (having  square,  cir- 
cular, triangular  links)   of  the  proper  color. 

Finally,  average  curves  as  well  as  maximum  and  minimum  curves 
are  drawn  for  the  various  colors  and  forms  of  marks. 

Maximum  and  minimum  curves  should  not  represent  the  very  best 
and  the  very  worst  possibilities ;  they  should  represent  the  average  of 
very   good  and  very  bad   trees. 

The  graphic  method  is  more  reliable,  because  less  depending  on  mere 
figures,  than  the  mathematical  method.  Both  methods  are  frequently 
combined. 

A  number  of  complete  tree  analyses  furnishes  more  reliable  results  than 
a  large  number  of  mere  volume  measurements  because  it  yields  more 
reliable  curves  (guide-curves)  of  development  for  one  and  the  same  lo- 
cality, and  because  it  prevents  the  forester  from  drawing  curves  of  growth 
at  random. 

If  the  sample  trees  (or  sample  logs)  are  sawn  up  at  a  saw  mill  where 
the  lumber  is  properly  graded  according  to  the  inspection  rules  prevailing 
for  the  species  in  question,  the  volume  tables  may  also  give  the  actual 
average  output  of  specified  trees  in  lumber  of  the  various  grades. 


SECTION  II.— INCREMENT  OF  A  WOOD. 
PARAGRAPH    XCI. 

INCREMENT   OF  FORESTS. 

The  volume  increment  of  the  virgin  forest  is  on  the  whole  nill. 

In  America  the  value  increment  of  a  primeval  forest  is  based  more  on 
a  price  increment  of  stumpage  than  on  a  volume  increment  of  trees.  The 
volume  increment,  in  addition,  can  scarcely  be  ascertained  with  sufficient 
accuracy  for  a  given  piece  of  forest  at  a  reasonable  expense. 

In  second  growth  forests,  on  the  other  hand,  say  in  Virginia,  an  abso- 
lute knowledge  of  the  productiveness  of  the  forest  renders  forestal  invest- 
ments safer  in  the  eyes  of  the  owner ;  and  the  safety  of  the  investment  it  is 
which  alone  can  tempt  the  capitalist  to  invest  in  forestry.     A  knowledge  of 


60  Forest  Mensuration 

the  increment  in  second  growth  woodlands  can  be  obtained  from  tabulated 
statements  ("yield  tables")  showing  the  rate  of  growth  for  woodlands  of 
a  given  species  in  a  given  locality.  Under  normal  yield  tables  are  under- 
stood such  tables  which  give  the  rate  of  growth  for  even-eged,  pure,  nor- 
mally stocked,  well  thinned  woodlots  for  given  localities  (compare  Para- 
graph  LIII.   and  XCIV..). 

Such  normal  yield  tables  are  constructed  abroad  for  beech,  pine,  spruce, 
fir  and  oak.  In  this  country  they  exist  only  in  Pinchot's  and  Graves' 
yield  tables  for  white  pine.  In  America,  pure  even-aged  woods  are  found 
in  rare  cases  only  (taeda,  echinata,  rigida,  jack  and  longleaf  pines,  tama- 
rack, coppicewood). 

In  the  construction  of  normal  yield  tables  the  following  points  require 
consideration : 

i.     The  different  methods  of  construction    (Paragraph  XCIL). 

2.  The  combination,  interpolation,  adjustment  and  correction  of  the 
results    (Paragraph  XCIIL). 

3.  The  contents  and  use  of  yield  tables   (Paragraph  XCIV.). 


PARAGRAPH   XCIL 

METHODS    OF    CONSTRUCTION    OF    NORMAL    YIELD   TABLES. 

Normal  yield  tables  may  be  based  on : 

A.  Repeated  survey  of  some  typical  woodlots  during  their  entire  life- 
time. » 

B.  Repeated  survey  of  different  woods  standing  on  an  equal  quality 
of  soil,  during  a  period  of  years  equal  at  least  to  the  longest  difference  in 
age  found  amongst  them. 

C.  One-time,  simultaneous  survey  of  a  very  large  number  of  woods  of 
different  ages  standing  on  different  qualities  of  soil.  Missing  links  are 
here  obtained  by  graphic  or  mathematical  interpolation  (Paragraph 
XCIIL). 

If  tables  are  constructed  by  repeated  survey  of  several  woods  (B),  it 
is  often  found  that  the  links  cross  one  another  for  unexplainable  reasons. 

PARAGRAPH    XCIIL 

GATHERING    DATA    FOR    NORMAL    YIELD    TABLES. 

In  order  to  see  whether  or  not  two  woods,  in  the  case  C  of  the  pre- 
ceding paragraph,  belong  to  the  same  chain  of  growth,  two  methods  are 
in  use : 

a.  The  horn  or  curve  method,  after  Baur. 

b.  The  stem  analysis  method. 


Forest  Mensuration  61 


Remarks  on  a: 


The  contents  and  age  of  all  woods  (normal)  surveyed  are  plotted  in  a 
diagram,  the  age  forming  the  abscissa  and  the  volume  the  ordinate  of  the 
system. 

Curves  are  then  drawn  outlining  the  maxima  and  minima  of  growth 
observed. 

The  horn-shaped  space  between  these  curves  is  divided  into  a  number 
of  sectors  equal  to  the  number  of  yield  classes  to  be  distinguished.  The 
middle  line  of  each  sector  illustrates  the  productiveness  of  its  class. 

The  average  height  growth  is  obtained  in  a  similar  way,  the  height  data 
forming  the  ordinates  in  a  system  of  co-ordinates. 

Baur  finds  that  the  allotment  of  a  given  plot  to  a  volume-sector  corre- 
sponds with  its  allotment  to  a  height  sector.  In  other  words,  the  height 
is,  after  Baur,  an  absolutely  reliable  indicator  of  the  quality  of  the  soil, 
or,  what  is  the  same,  of  the  yield  class. 

The  growth  of  sectional  area,  height  and  volume  being  known,  the 
development  of  the  form  factors  for  the  various  sectors  is  readily  ob- 
tained from  the  fraction 

sXh 

Remarks  on  b: 

An  analysis  of  the  average  stems  in  lots  surveyed  would  not  throw 
any  light  on  their  connection  as  members  of  one  and  the  same  chain 
of  observation.  After  Robert  Hartig,  the  200  strongest  trees  are  analyzed. 
After  Wagener,  the  ideal  cylinders  merely  of  these  200  strongest  stems 
are  analyzed  by  ascertaining  their  height  growth  and  their  diameter 
growth  at  breast  height.  Weise  and  Schwappach  are  satisfied  with  an 
analysis  of  the  heights  merely  of  the  200  best  stems. 

The  selection  of  sample  plots  is  not  easy,  even  in  second  growth  raised 
under  forestal  care.  A  valuation  survey  establishes  for  each  plot  the 
number  of  stems  and  the  sectional  area  for  each  diameter  class  of  stems 
(usually  divided  into  5  classes)  ;  further,  the  average  age  and  the  average 
height  of  the  plot.  The  volume  is  then  figured  out,  usually,  according 
to   the   Draudt-Urich   method. 

The  experiment  stations  maintained  by  the  European  Governments 
control  the  growth  of  a  large  number  of  experimental  plots,  which  should 
not  be  smaller  than   y2  acre  each. 

The  sample  plots  are  corner  marked,  and,  more  recently,  the  individual 
trees  contained  therein  are  numbered  consecutively.  Surveys  of  these 
plots  are  made  every  five  years.  The  point  of  measurement  is  indicated  by 
a  chalk  line. 

In  America  normal  sample  plots  have  not  been  established  as  yet  by 
the  Bureau  of  Forestry  in  second  growth.  The  sample  plots  at  Biltmore 
do   not   represent   a   normal    second   growth. 


62  Forest  Mensuration 

PARAGRAPH    XCIV. 

NORMAL   YIELD   TABLES,   THEIR   PURPOSES    AND   CONTENTS    ABROAD. 

Normal  yield  tables  are  especially  used  for  the  following  purposes: 

i.     To  ascertain  the  quality  of  the  soil   (c.  g.,  for  taxation). 

2.  To  ascertain  the  volume  of  the  growing  stock. 

3.  To  ascertain   future  yields   of  the   forest. 

4.  To  solve  problems  of  forest  finance,  especially  those  of  forest  ma- 
turity   (length  of  rotation). 

German  normal   yield  tables  have  the   following  contents : 

A.  Tables  for  the  main  forest — the  secondary  forest  comprising  such 

trees  on  the  same  lot  as  are  about  to  be  removed  by  way  of  thin- 
ning : 

(1)  Age,  graded  at  five  year  intervals. 

(2)  Number  of  trees. 

(3)  Sectional  area  at  chest  height,  inclusive  of  bark. 

(4)  Average  diameter. 

(5)  Average  height  and  height  increment. 

(6)  Volume  in  cubic  measure  arranged  according  to  assortments 

as  logs,  fuel,  bark,  etc. 

(7)  Periodical   and  average  annual  volume  increment. 

(8)  Increment  percentage. 

(9)  Form  factor. 

(10)     Normal   growing   stock. 

B.  Tables  for  the  secondary  forest,  giving  merely  its  vol ume,»  which, 
as  stated,  is  to  be  removed  by  way  of  thinning. 

Circular  445  of  the  Bureau  of  Forestry  defines  "future  yield  tables"  as 
follows :  "A  tabular  statement  of  the  amount  of  wood  which,  after  a 
given  period,  will  be  contained  in  given  trees  upon  a  given  area  expressed 
in  board  feet  or  some  other  unit." 


PARAGRAPH    XCV.    **«■*«  STVm  »r  \»  *    «* 

RETROSPECTIVE    YIELD    TABLES. 

In  "retrospective"  yield  tables  an  attempt  is  made  to  rebuild  the  grow- 
ing stock  as  it  was  before  lumbering  from  the  stumps  found  on  the 
ground  and  from  stem  analyses  of  the  trees  now  standing.  Prerequisite 
is  a  knowledge  of  the  year  in  which  lumbering  took  place  and  of  the 
conditions   of   growth   since   prevailing. 

Method   of   proceeding: 

1.  Make  stem  analyses  and  construct  tree  volume  tables,  showing  the 
probable  contents  of  trees  for  stumps  of  a  given  diameter  and  for  given 
diameters  b.  h. 


Forest  Mensuration  63 

2.  On  land  cut  over  n  years  ago,  find  by  valuation  survey  and  stem 
analyses : 

a.  The  present  volume  "F." 

b.  The  volume  "y"  of  the  trees  now  standing  as  it  was  "n"  years  ago 
with  the  help  of  tree  volume  tables. 

c.  From  the  stumps  the  volume  "x"  of  the  trees  logged  "n"  years  ago. 

3.  A  product  of  "F"  units  (with  an  undergrowth  not  fit  for  logging) 
has  been  derived  in  "n"  years  from  an  original  stand  aggregating  "y" 
plus   "x"   units  of  volume. 

4.  Grouping  hundreds  of  sample  plots  together,  yield  tables  for  local 
use  are  obtained.  Misleading  is,  of  course,  the  multiplicity  of  conditions 
(mixture  of  species,  soils,  original  stands,  pasture  and  fire)  surrounding 
a  second  growth  which  check  the  applicability  and  the  combination  of 
the  tables   found. 

The  tables  are  way  signs,  not  ways,  toward  a  true  knowledge  of  the 
productiveness  of  cut-over  woodlands. 


PARAGRAPH  XCVI. 

YIELD   TABLES    OF   THE    BUREAU    OF   FORESTRY. 

Bureau  yield  tables  are  meant  to  show  the  growth  on  cut-over  land 
occurring  within  the  next  10,  20  or  30  years,  if  a  tract  is  logged  to  a 
10",  12"  or  14"  (or  any  other)  limit.  Bureau  yield  tables  are  based  on 
tree  volume  tables  and  on  an  account  of  the  numbers  of  tree  individuals 
found  in  the  various  age  classes  of  forest,  viz.,  diameter  classes  of  trees. 

The  influence  of  the  different  qualities  of  soil  on  tree  growth  is  not 
given,  only  one  average  volume  table  being  constructed.  The  volume 
tables  show  the  number  of  years  which  a  tree  requires  to  increase  its 
diameter  b.  h.  by  one  inch.  The  volume  tables  record,  in  addition,  the 
volume  increase  corresponding  with  such  diameter  increase.  Applying 
these  findings  to  the  stumpage  presumably  left  after  logging,  the  volume 
can  be  ascertained  which  is  expected  to  be  on  hand  10,  20  or  30  years 
later.  The  volume  growth  is  forecasted,  as  if  it  were  taking  place  under 
primeval  conditions. 

The  Bureau  neglects  entirely  the  death  rate  of  trees,  due  to  natural 
causes  and  especially  high  amongst  seedlings  and  saplings,  or  else  due 
to  the  logging  operations  themselves.  The  results  forecasted  in  this  way 
must  be  invariably  too  high. 

Pinchot's  Spruce  Tables  (The  Adirondack  Spruce,  p.  77)  are  based  on 
similar  premises : 

a.  Construct  volume  tables  by  stem  analysis  (stump-analysis)  on  land 
cut  over  for  a  second  time,  thus  showing  rate  of  growth  for  trees  left 
standing  at  the  first  cut. 

b.  Construct  tables,  by  actual  measurements  in  the  woods,  giving  the 


64 


Forest  Mensuration 


number  of  trees  of  the  various  diameters,  composing  a  stumpage  of  from 
1,000  to   12,000  feet  board  measure. 

c.  Predict  the  number  of  trees  and  their  exact  diameters  to  be  found 
10,  20  or  30  years  after  logging,  according  to  severity  of  logging  (diam- 
eter limit). 

d.  With  the  help  of  the  volume  tables,  give  the  contents  of  these  trees. 

In  these  tables  as  well,  the  death  rate  amongst  trees  is  disregarded.  For 
normal  death  rate,  compare  Pinchot's  "White  Pine,"  p.  80,  ff;  also  remarks 
at  end  of  Paragraph  LIV. 


PARAGRAPH    XCVII. 


THE    INCREMENT    OF    A    W00DL0T. 


The  current  as  well  as  the  annual  average  increment  of  normal,  even- 
aged  woods  culminates  at  a  much  earlier  date  than  the  increment  of  the 
trees  composing  such  woods.  The  explanation  lies  in  the  death  rate  of 
the  trees. 

Under  a  close  crown  density  in  even-aged,  normal  woods,  the  stronger 
half  of  the  trees  yield,  from  the  pole  stage  on,  practically  all  the  incre- 
ment, the  weaker  half  of  the  trees  being  almost  inactive. 

The  better  the  quality  of  the  soil,  the  earlier  occurs  the  culmination  of 
the  increment;  consequently,  on  good  soil,  shorter  rotations  are  apt  to  be 
advisable   than   on   poor   soil. 

Light  demanding  (intolerant)  species  show  an  earlier  culmination  than 
shade   bearers    (tolerant)    species. 

For  white  pine  woods,  after  Pinchot,  the  years  of  increment  culmina- 
tion are  as  follows : 


Culmination 

For  entire  volume  with 
bark  in  cu.  ft. 

For  volume  Doyle  in 
ft.  b.  m. 

of 

I. 

II. 

III. 

I. 

II. 

III. 

Current  inert.. .  . 
Average  inert .  .  . 

40th 
60th 

50th 
80th 

60th  yr. 
1  ooth  yr. 

70th 
i35th 

70th 
1 60th 

noth  yr. 
210th  yr. 

I  denotes  best;  II  denotes  medium,  and  III  denotes  poorest  quality  of 
soil. 

The    increment   of   a    woodlot,    whether    normal    or    abnormal,    can    be 
obtained : 

a.  With  the  help  of  yield  tables. 

b.  By  special   investigations  made  into  the  rate  of  growth  of  sample 
trees    (Paragraph  XCVIII.). 


Forest  Mensuration  65 

c.  With  the  help  of  the  average  annual  increment  of  the  woodlot  (Par- 
agraph XCIX.)- 

The  increment  of  a  past  period  is  never  exactly  equal  to  that  of  a 
future  period,  unless  the  age  of  the  woods  is  close  to  that  year  at  which 
the  increment  culminates.  The  increment  percentage  during  a  past  period 
is  always  larger  than  the  increment  percentage  during  a  coming  period 
(aside  of  temporary  increase  due  to  light-increment). 

The  general  laws  (Paragraph  LXXV.)  relative  to  the  culmination, 
increase  and  decrease  of  increment  hold  good  for  the  volume  increment 
of  woodlots  as  well  as  for  that  of  trees. 


PARAGRAPH   XCVIII. 

ASCERTAINING    THE    INCREMENT    OF    WOODLOTS    BY     SAMPLE    TREES. 

The  current  annual  volume  increment  and  the  volume  increment  per- 
centage of  a  wood,  from  which  its  maturity  largely  depends,  can  be  cor- 
rectly found  only  by  a  valuation  survey,  combined  with  an  investigation 
into  the  present  rate  of  growth  exhibited  by  a  number  of  sample  trees. 

Borggreve  recommends  to  gauge  the  increment  of  the  sample  trees  by 
the  Schneider  increment  percentage.     This   is   usually  insufficient. 

The  correct  volume  increment  percentage  p  of  a  woodlot  is  obtained 
from  the  volume  increment  percentage  pi,  pn,  p3,  p<  and  ps  of  the  class  sam- 
ple trees — which  represent  class-volumes  vi,  vj,  vs,  V4  and  x-0 — as 

vi  Pi  +  vj  P2  4-  v3  p3  +  v4  p4  +  v5  p5 


Vl     +  V2    4"    V3    +    V4    +    V5 

Where  the  form  heights  of  the  classes  differ  slightly  only,  the  sectional 
areas  of  the  classes  may  be  substituted  for  the  volumes  of  the  classes. 

Again,  where  classes  of  equal  sectional  area  are  formed  (after  Robert 
Hartig),  there  the  volume  increment  per  cent,  of  the  woodlot  equals  the 
arithmetic  mean  of  the  volume  increment  percentages  of  the  sample 
trees,  so  that 

Pi  +P2  +  Ps  +  P4  +  P5 


PARAGRAPH    XCIX. 

CURRENT    INCREMENT    ASCERTAINED    FROM     AVERAGE     INCREMENT. 

Within  certain  limits,  a  short  time  previous  and  a  short  time  after  the 
culmination  of  the  average  annual  increment,  the  annual  average  incre- 
ment equals  the  current  increment  and  can  be  used  in  its  place  as  a  basis 
for  yield  calculation.  European  Governments  frequently  prescribe  this 
modus  operandi  for  yield  forecasts  in  working  plans. 


66  Forest  Mensuration 

CHAPTER  IV.— LUMBER 

PARAGRAPH     C. 

UNITS    OF    LUMBER    MEASUREMENT. 

For  rough  lumber  one  inch  thick,  or  thicker,  the  unit  of  measure,  known 
as  one  foot  board  measure,  is  a  square  foot  of  lumber  one  inch  thick. 
*"v^~""*-  (,"i^)This  unit  is  the  i/i2th  part  of  a  cubic  foot. 

■    For    rough    lumber    thinner    than    one    inch,    the    unit    of   measure,    also 
-,  $  known  as  one  foot  board  measure,  is  the  superficial  square  foot,  and  the 
thickness  of  the  lumber  is  here  entirely  disregarded. 

All  dressed  stock  is  measured  and  described  as  if  it  were  the  full  size 
of  the  rough  lumber  necessarily  used  in  its  manufacture.  "Inch  flooring," 
e.  g.,  is  actually  13/16  inch  thick ;  and  "^  inch  ceiling"  is  actually  5/16 
inch  thick. 


Standard  thicknesses  are: 

tff  »  J  •  h  -'  8'  *'  J>  Ii'  x2'  2'  22>  3  x4  • 

Standard  lengths  are: 

in  hardwoods  6  to  16  feet; 

in  softwoods  10  to  24  feet. 
In  both  cases,  lengths  in  even  feet  (not  in  odd  feet)  are  required. 
A  shortness  of  1"  or  2"  in  the  length  of  hardwood  boards  is  disregarded. 

Standard  defects  are : 

I.  In  hardwoods:  one  sound  knot  of  1  \"  diameter; 

one  inch  of  bright  sap ;  ► 

one  split,  its  length  in  inches  equalling  the  contents  of 
the  board  in  feet  b.m. 

II.  In  softwoods  :  sound  knots,  viz. : 

(a)  pin-knots  of  not  over  J"  diameter; 

(b)  standard  knots  of  not  over  ij"  diameter  ; 

(c)  large  knots  of  over  i\"  diameter; 

pitchpockets,  viz.  : 

(a)  small  pitchpockets  J"  wide; 

(b)  standard  pitchpockets  up  to  |"  wide  and  up  to  3' 
long; 

pitchstreaks,  viz. : 

(a)  small  pitchstreaks  not  wider  than  jl5  the  width  and 
not  longer  than  }■  the  length  of  board  ; 

(b)  standard  pitchstreaks  with  dimensions  up  to  twice 
as  large  as  given  under  (a); 

sap,  viz..: 

(a)  bright  sap ; 

(b)  blued  sap ; 

splits,  wane,  scant  width,  tongues,  less  than  y\"  long. 


Forest  Mensuration  67 

The  point  at  which  a  defect  is  located  greatly  influences  its  effect  on 
the  grade  of  the  lumber. 

The  two  faces,  the  two  edges  and  the  two  ends  of  a  board  must  be 
parallel.  In  case  of  unevenness,  the  thinnest  thickness,  the  narrowest 
width   and  the  shortest  length  are   measured. 

Lumber  is  measured  with  the  help  of  a  lumber  rule  (Lufkin  rule)  which 
yields  for  inch  boards  of  given  lengths  and  given  width  the  correspond- 
ing contents   in   feet  b.  m. 

In  measuring  the  widths,  fractions  of  an  inch  are  neglected  in  rough 
lumber. 


PARAGRAPH    CI. 

INSPECTION    RULES     AND    NOMENCLATURE. 

The  lumber  inspection  prevailing  in  a  given  market  is  governed  by 
local  custom  or  by  agreement  within  the  body  of  local  associations  of 
lumbermen. 

The  tendency  of  all  inspection  rules  is  directed  toward  a  gradual  lower- 
ing of  rigidity. 

The  wholesaler's  inspection  is  generally  stiffer  than  that  of  the  manu- 
facturer. Diversity  of  rules  is  a  sadly  demoralizing  element  in  lumber 
circles. 

Lumber  sawn  for  special  purposes  {e.  g.,  wagon  bolsters)  must  be  in- 
spected with  a  view  to  its  adaptability  for  such  special  purpose. 

A.    Hardwood.     The  grade  of  a  board  depends  on 

1.  Its    width    and    length; 

2.  Its  standard  defects ; 

3.  The  percentage   of  clear  stock  contained   therein ; 

4.  The  number  of  cuttings  yielding  such  clear  stock. 

The  following  table  shows  average  specifications  prevailing  for  the 
various  grades  of  hardwood  lumber  in  the  U.  S.  markets. 

The  defects  specified  invariably  indicate  the  coarsest  stock  admissible 
in  a  given  grade. 


68 


Forest  Mensuration 


Hardwood 

Lumber  Specifications. 

Designation 

Minimum 

Actual 

Allows  of 

of 
Grade. 

Len'h 
feet. 

Wi'th 

inch- 
es. 

Length 
feet. 

Width 
inches. 

No.  of 
standard 
defects. 

Rate 
of  clear 
stock. 

Con'd  in 
c't'ngsnot 
more  than 

Firsts 

Seconds 

IO 

8 

IO 

8 
8 
6 

i  o  &  over 
i  o  &  over 

8 

8 
i  o  &  over 
io  &  over 
i  o  &  over 
io  &  over 

8&9 
io  &  over 

8&9 
io  &  over 

6&  7 

8&9 

IO  &  II 

1 2  &  over 

none 
one 
none 
one 
none 
one 
two 
three 

"3 

a 
u 

V 

a 

o 

o 

In 

Ph 

No.  i  Com... 

6 

8 

6 

4 

6 
6 
8 
8 
8&  io 

12  to  1 6 

6  to  8 
9  &  over 

4 

5 
6  &  over 
6  &  over 

none 
one 
none 
one 

all 
all 
all 
all 

§ 

I 
I 

I 
I 

2 

3 

No.  2  Com.. . 

6 

3 

6  to  io 
12  to  1 6 

i 

3 
4 

No.  3  Com.. . 

4 

3 

\ 

B.  Softwoods.  Softwood  lumber  is  inspected  from  its  best  side 
Under  "edgegrain"  is  understood  lumber  the  face  of  which  forms  an*  angle 
of  less  than  45  degrees  with  the  plain  of  the  medullary  rays  contained  in 
the  board.  All  other  lumber  is  termed  "flat  grain"  or  "slash  grain,"  also 
"bastard  grain." 


I.  Finishi?ig  Lumber,  1"  to  2"  thick,  dressed  one  or  two  sides. 

1.  First  and  second  clear, 

up  to  8"  wide  ;  absolutely  clear ; 
10"  wide;  one  small  defect  permitted; 

12"  and  over  wide;  \  of  stock  may  have  one  standard  knot  or 
its  equivalent. 

2.  Third  clear, 

allows  of  twice  as  many  defects. 

II.  Flooring,  1"  thick  and  3"  or  4"  or  6"  wide  before  dressing;  either 
with  hollow  back  or  with  solid  back ; 

1.  A,  B  and  C  flat  grain  flooring ;  wherein  "A"  is  clear  and  "B"  al- 

lows of  one  or  two  standard  defects  ; 

2.  A,  B  and  C  edgegrain  flooring ;  with  the  same  allowance ; 

3.  No.  1  and  No.  2  fence  flooring. 


Forest  Mensuration  69 

III.  Ceiling,  f,  $  and  |  inch  thick;  3,  or  4,  or  6  inches  wide. 

1.  "A"  ceiling  and  "B"  ceiling,  with  small  defects  only; 

2.  No.  1  and  No.  2  common  ceiling,  with  one  and  two  standard  de- 

fects, or  their  equivalent. 

IV.  Drop  Siding,  which  is  either  "shiplapped"  or  "tongued  and  grooved;" 

it  is  %"  thick  and  3^  or  5J  inches  wide.     Grades  A,  B  and  No.  1 
common. 

V.  Bevel  Siding,  which  scales  Ty  at  the  thin  edge  and  \"  at  the  thick 
edge,  resawn  from  stock  dressed  to  £$"  x  5$".     Grades  as  under  IV. 

VI.  Partition,  measuring  f "  x  3J"  or  |"  x  5I".     Grades  as  under  IV. 

VII.  Common  Boards,  graded  as  No.  1,  No.  2  and  No.  3  common  boards, 
8",  10"  or  12"  wide,  dressed  one  or  two  sides,  or  rough. 

VIII.  Fencing,  graded  as  No.  1,  No.  2  and  No.  3  fencing,  3",  4"  or  6"  wide. 
The  grade  "No.  3"  includes  defective  lumber  with  knot-holes,  red 
rot,  very  wormy  patches,  etc.,  on  \  of  the  length  of  the  board. 
Fencing  is  either  dressed  or  rough. 


CHAPTER  V.— STUMPAGE  VALUES 

PARAGRAPH  CII. 

STUMPAGE  VALUES. 

Forestry  is  a  business ;  the  forest  largely  represents  its  business  invest- 
ment ;  its  purpose  is  the  raising  of  money,  of  dividends. 

Thus  it  is  with  investments  and  the  dividends  therefrom  that  the  fores- 
ter is  concerned;  and  it  is  the  task  of  "forest  finance"  and  "forest  manage- 
ment" to  ascertain  the  factors  and  to  regulate  the  components  of  such 
investments. 

Forest  mensuration,  as  a  subsidiary  to  forest  management,  may  well 
devote  a  chapter  to  the  measurement  of  the  stumpage  value  of  trees. 

Stumpage  value  is  the  price  which  a  tree  brings  or  should  bring  if  it 
were  sold  on  the  stump. 

The  stumpage-value  of  a  tree  depends  on  the  value  of  the  lumber  con- 
tained therein  and  obtained  therefrom,  deducting  the  total  expense  of 
lumber  production  (logging,  milling,  shipping,  incidentals.) 

Since  the  value  of  lumber  fluctuates,  as  well  as  the  cost  of  production, 
stumpage  values  are  subject  to  continuous  variation.  The  tendency  of 
stumpage  prices,  all  over  the  world,  is  a  tendency  to  rise — especially  so 
in  countries  of  rapid  development,  rapid  increase  of  population  and  in- 
adequate provisions   for  re-growth. 


70  Forest  Mensuration 

The  cost  of  production  is  composed  about  as  follows : 

i.     Expense   of   logging   and   log   transportation,    varying   locally   be- 
tween $2  and  $5  per  i,ooo'  b.  m. 

2.  Expense  of  milling,  varying  between  $1.50  and  $5  per  1,000'  b.  m. 

3.  Expense    of    freightage    of    lumber    to    the    consuming    market, 

amounting  per  1,000'  b.  m.  to  $1.50  for  very  short  hauls;  to 
$12  for  a  haul  from  Atlanta  to  Boston;  to  $21  for  a  haul  across 
the  continent  from  Portland   (Oregon)   to  New  England. 

Freight  rates  have,  in  the  long  run,  a  decided  downward  tendency. 
Still,  with  a  majority  of  the  lumber  produced  in  the  U.  S.,  the  item 
"freight"   forms  the  chief  expense  of  production. 

For  Pisgah  Forest  a  reduction  of  freight  rates  equalling  1  cent  per  100 
lbs.  involves  a  net  gain  for  the  owner  of  approximately  $60,000.  In  this 
possibility  lies  one  of  the  strongest  arguments  for  conservative  lumbering. 

An  increase  of  the  price  of  lumber  from  $20  to  $21  at  the  place  of  con- 
sumption endears  the  lumber  to  the  consumer  by  5% ;  the  owner  of  the 
forest  now  valuing  his  stumpage  at  $5  will  eventually  experience  this  in- 
crease as  a  20%  increase  of  stumpage  values. 

The  only  factors  of  stumpage-values,  which  the  owner  himself — unaided 
by  the  development  of  the  country — may  influence,  consist  in  the  expense 
of  logging  and  log  freighting,  and  in  the  expense  of  milling,  the  former 
largely  depending  on  the  quality  of  available  means  of  transportation,  the 
latter  governed  by  the  quality  of  the  sawmill. 

In  ascertaining  the  stumpage-value  of  a  tree  the  forester  considers : 

a.  The  cost  per  1,000'  b.  m.  of  logging  it,  of  milling  it  and  of  freight- 

ing its  timber; 

b.  The  volume  of  timber  contained  in  the  tree,  by  grades ; 

c.  The  value  of  such  lumber,  by  grades. 

If  a  tree  contains 
45%  of  lumber  worth  $31  per  1,000'  b.  m. 

It  is  necessary  to  find  Stoetzer's  constant  factor  of  increment  or  to 
ascertain  the  relative  increment  of  the  sectional  areas  of  the  sample  trees 
at   0.45    of   their   heights. 

35%  of  lumber  worth  $21  per  1,000'  b.  m. 

15%  of  lumber  worth  $16  per  1,000'  b.  m. 

5%  of  lumber  worth    $8  per  1,000'  b.  m. 

then,  the  lumber  value  of  the  tree,  per  1,000'  b.  m.,  is 

45  x  31  +  35  x   21  +  15  x   if,  +  5  x  8 


100 


=  $24.10 


Deducting  from  this  figure  the  expense  of  logging,  milling  and  freight- 
ing, the  actual  stumpage-value,  per  1,000'  b.  m.,  is  derived. 

The  actual  prices  paid  for  stumpage  in  the  U.  S.  fall  deeply  below  the 
figures  which  a  test-calculation  is  apt  to  yield. 


Forest  Mensuration 


71 


This  discrepancy  may  be  explained,  above  all,  by 

Ignorance   of  owners   of  stumpage ; 
Agents'  and  dealers'  profits ; 
Incidental  expenses  overlooked. 

Stumpage-values  show  a  rapid  decrease  with  the  increase  of  the  dis- 
tance separating  the  tree  from  the  nearest  railroad  or  stream. 

The  grades  of  lumber  and  their  proportion  obtainable  from  logs  of 
given  species,  diameter  and  soundness  (including  presence  and  location 
of  defects)  can  be  ascertained  only  by  test-sawing  in  the  mill. 

This  has  been  done  in  1896  for  yellow  poplar  at  Biltmore  (bandsaw 
mill).  The  stumpage-values  then  ascertained  are  shown  by  the  follow- 
ing table : 

Market  Value  of  Poplar  Stumpage  in  Western  North  Carolina,  Per 

Tree,  in  Cents. 


<*-! 

Under  good 

Jnder  average 

Under  poor 

O 

4> 

conditions. 

conditions. 

conditions. 

be 

Logging  and  Milling 

Logging  and  Milling 

Logging  and  Milling 

<u  b 

.  ui 

expenses   being  per 

■   t/j 

expenses  being  per 

•  in 

expenses   being  per 

5& 

H_= 
n  0 

1000  feet  B.  M. 

Eg 

1000  feet   B.  M. 

.So 

1000  feet  B.  M. 

< 

S-S 

$9 

Sio 

$n 

O.S 

$9 

$10      $11 

P.S 

$9      Sio 

$11 

IOo 

Nega- 

Nega- 

Nega- 

Nega- 

Nega-   Nega- 

Nega-  Nega- 

Nega- 

tive. 

tive. 

tive. 

tive. 

tive. 

tive. 

tive. 

tive. 

tive. 

I20 

18.8 

8 

« 

«. 

« 

<< 

« 

« 

■  < 

« 

140 

21  .3 

40 

25 

" 

18 

2 

4 

" 

" 

" 

" 

" 

160 

23-5 

105 

7  2 

2 

20 

4 

22 

5 

" 

" 

" 

" 

i  So 

25-7 

265 

170 

98 

2  2 

4 

67 

35 

" 

" 

" 

" 

200 

27.7 

445 

325 

23O 

24 

3 

160 

103 

3D 

18 

5 

" 

" 

" 

220 

29.6 

620 

465 

350 

2h 

0 

287 

200 

109 

20 

O 

7 

" 

" 

240 

27 

5 

430 

330 

210 

21 

3 

27 

3 

" 

260 

460 

330 

22 

1 

60 

25 

" 

280 

45 

" 

300 

5 

320 

30 

Footnote  :  Dots  below  a  column  of  figures  indicate  higher  values,  not 
specifically  ascertained. 

The  values  above  the  columns  of  figures  are  all  negative  and  were  not 
ascertained  specifically  either. 


It  is  to  be  hoped  that  similar  tests  will  be  made  for  our  leading  species 
on  a  large  scale  by  the  U.  S.  Forest  Service  or  by  the  various  associations 
of  lumber  manufacturers.  Conservative  forestry  as  a  business  badly  re- 
quires data  allowing  to  estimate  the  actual  value  of  logs,  and  hence  of 
trees,  if  the  uncertainty  of  financial  results  now  checking  the  progress  of 
conservative  forestry  in  America  is  to  be  definitely  reduced. 


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